Okay, this scenario is virtually impossible and unbelievably stupid but still, I just wanted to prove that it's possible:

Player 1's hand:
Briget, Eloxia, C Wing, Tino

Bridget is meant to keep Player 1 alive and the other three are just for the Defeat: abilities. Eloxia is needed for the KO.

Player 2's hand:
Sylvia Ld, Bernie, Esther, Drummond

A combination of low damage and lot of backlash.

Round 1:

Bernie beats Eloxia.
Bernie takes 2 backlash damage and poison is activated.
Bernie dels a total of 5 damage.

Player 1: 12 - 5 life = 7 life
Player 2: 12 - 2 life = 10 life

Round 2:
Bridget gives Player 1 one life. Player 1 has 8 life.
Syliva Ld beats Tino.
Sylvia Ld takes 3 backlash damage. Tino's ability deals 3 damage.
Since the minimum of the Berzerk bonus is hit, Player 1 will end up at 2 life.
Eloxia deals 1 poison damage.

Player 1: 7 + 1 - 6 life = 2 life
Player 2: 10 - 3 - 3 - 1 life = 3 life

Round 3:
Bridget gives Player 1 one life.
Esther beats C Wing.
C wing's Defeat: ability hits the minimum at 2 life.
Eloxia deals 1 poison damage.

Player 1: 2 + 1 - 1 life = 2 life
Player 2: 3 - 1 - 1 life = 1 life

Round 4:
Bridget gives Player 1 one life. Player 1 has 3 life.
Drummond beats Bridget.
Player 2 takes 2 damage. Player 1 has 1 life.
Esther's poison doesn't activate since it is under its minimum.
Eloxia deals 1 poison damage. Player 2 has 0 life.

Player 1: 2 + 1 - 2 life = 1 life
Player 2: 1 - 1 life = 0 life

There you go, A ZERO HIT KO!