Here is the full list of all 20 Impaler achievements.
Complete the game without gun kills
Unlock all upgrades
Score 20,000 or more 5 times
Complete the game without spike kills
Jump on top of a flying enemy
Unlock all weapons
Stomp and kill 5 enemies at once
Deliver an offering without pushing it.
Complete all stages and defeat the boss.
Score over 10,000
Slay every type of monster
Kill 5 enemies using exploding barrels
Overheat your weapon 10 times during a single run
Score over 1,000
Score over 5,000
Kill 6 enemies during bullet time