There are 2 methods to killing Krom.
1) Beserker/Hunter/Soldier. See video below, all credit to BronzeApples.
2) Lilith. Use her action skill to run pass enemies. When it ends and you are recharging, hide behind a hut or in a building where Krom and other enemies can not hit you. You may need to fight off some enemies while your action skill recharges. Keep doing this until you get to the very top where Krom is. Kill off the enemies near him and simply kill Krom from behind. If your health gets in danger, activate your action skill and just sit tight until it ends.
Once Krom is killed, the trophy will unlock.
Happy Hunting :)