It should be noted that the number of Animal Kings required for this achievement depend on the difficulty that you are playing on. On Easy, you are only required to kill 4, on Normal you will have to kill 6. On Hard, you will have to kill all 8.
Despite the fact that you won't be killing all 8 possible Animal Kings on Easy/Normal, killing the required amount for that difficulty will still count towards this achievement.
The Animal Kings are:
-Queen Bee (located in the forest northwest of Green Grass) - Accessible on all difficulties.
- Golem King (located in the Grey Cave, interact with the blue suit of armor) - NOT accessible on Easy.
- Lord of the Roots (located at the Scarlet River. There should be a visible plant somewhere in the southern area) - NOT accessible while playing on Easy.
- Bear King (in the first cave after exiting the Rocky Path's southern exit, heading towards Sapphire Cave) - NOT accessible on Easy difficulty.
- Twin Tigers (cave south of the swamp area where you recruit Karine) - Accessible on all difficulties.
- Ant King (in the Rocky Path area, take the south path when you see the three dwarves. Follow the path and inspect the hole in the wall) - Accessible on all difficulties.
- Rat King (located in the Sapphire Cave) - Accessible on all difficulties.
- Crocodile King (located in the Rogue Territory, there is a glowing tree you can examine to fight him) - NOT accessible while playing on Easy.