Here is the full list of all 13 Minimal Crypt Playtest achievements.
Finish the section "Cryptic Axioms"
Finish the section "Unstable Foundations"
Finish all the official levels
Switch level or section by hand
Create your first level
Create a level that takes 25 actions to solve
Create a level that takes 50 actions to solve
Add your first level from the community
Solve your first level from the community
Solve 10 levels from the community
Solve 50 levels from the community
Perform the ancient sequence