Here is the full list of all 16 One Life achievements.
Die 10 times.
Die 100 times.
Complete stage 1 for the first time.
Complete stage 2 for the first time.
Complete stage 3 for the first time.
Complete stage 4 for the first time.
Complete night 1.
Complete night 2.
Beat the final boss.
Start night 2.
Get blinded.
Kill a bomber by shooting its bomb.
Kill 3 enemies with a dash attack.
Teleport for the first time.
Hide inside the final boss's forehead.
Get a laser enemy to kill a bullet enemy.