Here is the full list of all 12 qomp2 achievements.
Complete chapter 2
Find a secret exit in any level
Complete chapter 1
Die 100 times
Complete the Introduction
Complete chapter 3
Complete chapter 4
Complete chapter 5
Collect 50% of every in-game collectible
Collect every in-game collectible
Complete Warlords without grabbing a checkpoint
Complete 2-6 in one life