Here is the full list of all 8 Puzzzle achievements.
The base game contains 4 achievements, and there is 1 DLC pack containing 4 achievements.
LISTEN TO MY BORING AUDIO LOG IN "ABOUT" IN THE MAIN MENU
COMPLETE THE GAME (VERSION 1.0)
WITNESS LEVEL 8
PUSH THE CUBE IN LEVEL 1
Get to level 86
Get to level 46.
Get to Introduction level 4.
Poke around the main menu a bit...