Genesis 3_15
I will put enmities between thee and the woman, and thy seed and her seed: she shall crush thy head, and thou shalt lie in wait for her heel.
The first allusion to the incarnations of the Blessed Virgin Mary and of her Son Jesus Christ in the Scripture was in Genesis 3:15.  It was called the Protoevangelium or the first announcement of the Messiah Redeemer and His mother and it goes this way:
 I will put enmities between thee and the woman, and thy seed and her seed: she shall crush thy head, and thou shalt lie in wait for her heel.  (Gen 3:15Douay Rheims Version)
Straight to the point, Genesis 3:15 was actually saying:
God will put enmities between Satan and Mary (already present in the eternal thought of God), and Satan’s seed and Mary’s seed: Mary shall crush Satan’s head, and Satan shalt lie in wait for her heel.
Enmity is defined as: positive, active, and typically mutual hatred or ill will.
Thus, God put everlasting enmities between Satan and Mary, making them antagonists forever.
Satan is everything evil: for he is the murderer from the beginning and the father of lies (Jn 8:44); the bringer of the Antichrist and the false prophet (2 Thes 2:8-9; Rev 13); the deceiver (2 Cor 11:3; Rev 12:9); the incessant accuser (Rev 12:10); the enemy (Mt 13:39; Lk 10:19); the disobeyer of God (Is 14:12-14KJV).
Mary is the antithesis of Satan: for she is the full of grace (Lk 1:28DRV); the mother of the Lord God Jesus Christ (Lk 1:43); the mother of the sinless and undeceiving Jesus (1 Pt 2:22); the mother of truth (Jn 14:6); the blessed among all women and generations (Lk 1:42, 48); the obeyer of God (Lk 1:38).
The perpetual animosities between Satan and Mary, between evil and good, are ever continual and even recorded in the last book of the Bible: Revelations 12, which in part have these accounts:
And his (Satan) tail drew the third part of the stars of heaven, and did cast them to the earth: and the dragon (Satan) stood before the woman (Mary) which was ready to be delivered, for to devour her child (Jesus) as soon as it was born.  (Rev 12:4, KJV, emphasis mine)
And when the dragon (Satan) saw that he was cast unto the earth, he persecuted the woman (Mary) which brought forth the man child (Jesus).  And to the woman (Mary) were given two wings of a great eagle, that she might fly into the wilderness, into her place, where she is nourished for a time, and times, and half a time, from the face of the serpent (Satan).  And the serpent cast out of his mouth water as a flood after the woman, that he might cause her to be carried away of the flood.  And the earth helped the woman, and the earth opened her mouth, and swallowed up the flood which the dragon cast out of his mouth.  And the dragon (Satan) was wroth with the woman (Mary), and went to make war with the remnant of her seed (faithful Christians esp. Catholics), which keep the commandments of God, and have the testimony of Jesus Christ.  (Rev 12:13-17KJV, emphasis mine)
 Non-Catholics are quick to react that it was not Mary who will crush the serpent’s head but her Son, Jesus Christ. And they readily quote Genesis 3:15 of their own translation of the Bible, the King James Version in this wise:
And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel.  (Gen 3:15King James Version)
However, Douay Rheims Version explained the discrepancy between the Catholic and Protestant Bibles in their footnote for Genesis 3:15 like so:
DRV Footnote, Genesis 3:15She shall crush: Ipsa, the woman; so divers of the fathers read this place, conformably to the Latin: others read it ipsum, viz., the seed. The sense is the same: for it is by her seed, Jesus Christ, that the woman crushes the serpent’s head.
Between the two versions, the Douay Rheims Version has the more accurate translation of Genesis 3:15.
In the King James Version, it was exclusively the woman’s (Mary’s) seed, Jesus Christ, which shall bruise the head of the serpent.  But when it was put under the scrutiny of the rest of the Bible, it was not so.  The Lord Jesus Christ assigned seventy more disciples (aside from His closest disciples) to tread (bruise, trample or crush) over all the power of the serpent, according to this passage:
And the seventy returned again with joy, saying, Lord, even the devils are subject unto us through thy name.  And he said unto them, I beheld Satan as lightning fall from heaven.  Behold, I give unto you power to tread on serpents and scorpions, and over all the power of the enemy: and nothing shall by any means hurt you.  Notwithstanding in this rejoice not, that the spirits are subject unto you; but rather rejoice, because your names are written in heaven.  (Lk 10:17-20KJV)
Does it mean Jesus Christ shall no longer tread or bruise the serpent’s head? 
No, the faithful disciples of Jesus Christ shall tread on the serpent’s (Satan’s) head but it will be the God of peace who will finally bruise Satan:
 And the God of peace shall bruise Satan under your feet shortly. The grace of our Lord Jesus Christ be with you. Amen.  (Rom 16:20)
Who is the God of Peace: the Father or Jesus Christ?
The God of Peace is the Father and the Prince of Peace is Jesus Christ, and yet the Father and Jesus Christ are one.
The Father is the God of Peace:
Now the God of peace, that brought again from the dead our Lord Jesus, that great shepherd of the sheep, through the blood of the everlasting covenant…  (Heb 13:20KJV)
The Lord Jesus Christ is the Prince of Peace:
For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace.  (Is 9:6KJV)
The God of Peace and the Prince of Peace are one:
I and my Father are one.  (Jn 10:30KJV)
So, in what way does Mary fits in in bruising the serpent’s head?
The Blessed Virgin Mary was the first and sublime disciple of the Lord Jesus Christ when she heard the word of God, believes it, keeps it, and observes it, as reported by Luke in this wise:
And in the sixth month, the angel Gabriel was sent from God into a city of Galilee, called Nazareth, To a virgin espoused to a man whose name was Joseph, of the house of David; and the virgin’s name was Mary.   And the angel being come in, said unto her: Hail, full of grace, the Lord is with thee: blessed art thou among women.   Who having heard, was troubled at his saying, and thought with herself what manner of salutation this should be.  And the angel said to her: Fear not, Mary, for thou hast found grace with God.  Behold thou shalt conceive in thy womb, and shalt bring forth a son; and thou shalt call his name Jesus.  He shall be great, and shall be called the Son of the most High; and the Lord God shall give unto him the throne of David his father; and he shall reign in the house of Jacob for ever.  And of his kingdom there shall be no end.   And Mary said to the angel: How shall this be done, because I know not man?   And the angel answering, said to her: The Holy Ghost shall come upon thee, and the power of the most High shall overshadow thee. And therefore also the Holy which shall be born of thee shall be called the Son of God.  And behold thy cousin Elizabeth, she also hath conceived a son in her old age; and this is the sixth month with her that is called barren: Because no word shall be impossible with God.  And Mary said: Behold the handmaid of the Lord; be it done to me according to thy word. And the angel departed from her.  (Lk 1:30-38DRV)
Mary’s cousin Elizabeth, under the inspiration of the Holy Spirit, testified that the Blessed Virgin Mother of God heard the word of God, believes it, keeps it, and observes it, as reported by Luke in this wise:
And it came to pass, that when Elizabeth heard the salutation of Mary, the infant leaped in her womb. And Elizabeth was filled with the Holy Ghost: And she cried out with a loud voice, and said: Blessed art thou among women, and blessed is the fruit of thy womb.  And whence is this to me, that the mother of my Lord should come to me?  For behold as soon as the voice of thy salutation sounded in my ears, the infant in my womb leaped for joy.  And blessed art thou that hast believed, because those things shall be accomplished that were spoken to thee by the Lord.  (Lk 1:41-45DRV)
And no less than the Lord Jesus Christ Himself testified that His mother Mary heard the word of God, believes it, keeps it, and observes it, as reported by Luke in this wise:
And it came to pass, as he spake these things, a certain woman of the company lifted up her voice, and said unto him, Blessed is the womb that bare thee, and the paps which thou hast sucked.  But he said, Yea rather, blessed are they that hear the word of God, and keep it.  (Lk 11:27-28DRV)
Contrary to the wrong understanding of the Protestants, Jesus did not dishonor Mary in the above passage, but rather, He exalted her.  In the said passage, the woman was praising the Lord Jesus Christ through her praising His mother who conceived and nursed Him.  But Jesus corrected the ordinary notion of the certain woman on her mother by immortalizing Mary, first and foremost, as the hearer, believer, keeper, and observer of the word of God, and as His most beloved and honored mother.
Therefore, the Blessed Virgin Mary being the first and sublime disciple of the Lord Jesus Christ was predestinated by God as the prime bruiser of the serpent’s head under the foot of her Son, Jesus Christ, in this wise:
I will put enmities between thee and the woman, and thy seed and her seed: she shall crush thy head, and thou shalt lie in wait for her heel.  (Gen 3:15DRV)
DRV Footnote on Genesis 3:15She shall crush: Ipsa, the woman; so divers of the fathers read this place, conformably to the Latin: others read it ipsum, viz., the seed. The sense is the same: for it is by her seed, Jesus Christ, that the woman crushes the serpent’s head.
 Three Blessed Among All Women Were Predestined To Bruise Their Enemy’s Head
In the Bible, there are three women called “blessed among women,” namely: Jael, Judith, and Mary. These three blessed women among women were foreordained to crush the heads of their enemies.
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Mary bruising the head of the serpent (Satan).
Mary
Of all the women created by God, only the Virgin Mary was called Blessed among all women by the Most Holy Trinity.
The Father through the angel Gabriel called Mary, “Blessed art thou among women:”
And in the sixth month, the angel Gabriel was sent from God into a city of Galilee, called Nazareth, To a virgin espoused to a man whose name was Joseph, of the house of David; and the virgin’s name was Mary.  And the angel being come in, said unto her: Hail, full of grace, the Lord is with thee:blessed art thou among women.  (Lk 1:26-28DRV)
The Holy Spirit through Elizabeth called Mary, “Blessed art thou among women;”
And it came to pass, that when Elizabeth heard the salutation of Mary, the infant leaped in her womb. And Elizabeth was filled with the Holy Ghost: And she cried out with a loud voice, and said: Blessed art thou among women, and blessed is the fruit of thy womb.  (Lk 1:41-42DRV)
The Son (cf Is 9:6), when His body was yet a zygote cleaved in the immaculate womb of Mary, inspired His mother to say, “All generations shall call me blessed:”
And Mary said: My soul doth magnify the Lord.  And my spirit hath rejoiced in God my Saviour.  Because he hath regarded the humility of his handmaid; for behold from henceforth all generations shall call me blessed (Lk 1:46-48DRV)
The Son, during the height of His earthly ministry, said of His mother Mary, “Blessed are they who hear the word of God, and keep it:”
And it came to pass, as he spoke these things, a certain woman from the crowd, lifting up her voice, said to him: Blessed is the womb that bore thee, and the paps that gave thee suck.  But he said: Yea rather, blessed are they who hear the word of God, and keep it.  (Lk 11:27-28DRV)
Being called “blessed among all women, and all generations” by the Triune God, the role of Marywas to bruise the head of Satan – the No. 1 Enemy of God.  This mission of Mary was premeditated by God in the beginning and He decreed it in the Protoevangelium which says:
I (the Triune God) will put enmities between thee (Satan) and the woman (the future Mary which was already present in the eternal thought of God), and thy seed (the Antichrist) and her seed (Christ): she (Mary) shall crush thy head (Satan’s), and thou shalt lie in wait for her heel.  (Gen 3:15DRV, emphasis mine)
jael-and-sisera1
Jael driving a peg in Sisera’s temple
Jael
Blessed among women be Jahel the wife of Haber the Cinite, and blessed be she in her tent.  He asked her water and she gave him milk, and offered him butter in a dish fit for princes.  She put her left hand to the nail, and her right hand to the workman’ s hammer, and she struck Sisara, seeking in his head a place for the wound, and strongly piercing through his temples.  At her feet he fell: he fainted, and he died: he rolled before her feet, and he lay lifeless and wretched.  (Judg 5:24-26DRV)
Judith_Beheading_Holofernes_by_Caravaggio
Judith beheading Holofernes by Caravaggio
Judith
And Ozias the prince of the people of Israel, said to her: Blessed art thou, O daughter, by the Lord the most high God, above all women upon the earth.  (Jdth 13:23DRV)
And Judith stood before the bed praying with tears, and the motion of her lips in silence, Saying: Strengthen me, O Lord God of Israel, and in this hour look on the works of my hands, that as thou hast promised, thou mayst raise up Jerusalem thy city: and that I may bring to pass that which I have purposed, having a belief that it might be done by thee.  And when she had said this, she went to the pillar that was at his bed’ s head, and loosed his sword that hung tied upon it.  And when she had drawn it out, she took him by the hair of his head, and said: Strengthen me, O Lord God, at this hour.  And she struck twice upon his neck, and cut off his head, and took off his canopy from the pillars, and rolled away his headless body.  And after a while she went out, and delivered the head of Holofernes to her maid, and bade her put it into her wallet.  (Jdth 13:6-11DRV)
Conclusion
Therefore, beyond reasonable doubt, the translation of Genesis 3:15 by the Douay Rheims Version where the Blessed Virgin Mary bruises the head of Satan is the true and faithful word of God:
Genesis 3_15_2
She shall crush: Ipsa, the woman; so divers of the fathers read this place, conformably to the Latin: others read it ipsum, viz., the seed. The sense is the same: for it is by her seed, Jesus Christ, that the woman crushes the serpent’s head.
I will put enmities between thee and the woman, and thy seed and her seed: she shall crush thy head, and thou shalt lie in wait for her heel.  (Gen 3:15DRV)
DRV Footnote on Genesis 3:15She shall crush: Ipsa, the woman; so divers of the fathers read this place, conformably to the Latin: others read it ipsum, viz., the seed. The sense is the same: for it is by her seed, Jesus Christ, that the woman crushes the serpent’s head.