Here is the full list of all 10 Kilonova achievements.
Clear all stages without taking any damage
Kill every enemy type
Kill ten enemies in total with your ultimate attack
Within 20 seconds of entering an arena, fill your entire ultimate bar
Watch the entire post-game credits without skipping
Perform an ultimate attack that kills only a single basic enemy
Kill 5 enemies with one use of your ultimate
Skip any arena
Kill an enemy while they are still spawning
Perform an ultimate attack 5 times in one arena