Here is the full list of all 25 Recompile achievements.
Complete the game with a HEX-Centric AI
Defeat the Hyperspider
Collect all the memories in the USER Biome
Complete TET Shield without killing a single enemy
Restore the OKT Biome
Fully upgrade Hacking abilities
Fully upgrade all Abilities
Restore the ICO Biome
Fully upgrade Traversal abilities
Survive a lethal fall
Restore the TET Biome
Fully upgrade Deletion abilities
Restore the HEX Biome
Kill 32 enemies
Install yourself
Collect all the memories in the TET Biome
Collect all the memories in the HEX Biome
Collect all the memories in the OKT Biome
Collect all the memories in the ICO Biome
Complete the game with an ICO-Centric AI
Complete the game with an OKT-Centric AI
Complete the game with a TET-Centric AI
Restore all Memories and complete the game with a Balanced AI
Hack 16 enemies
Complete TET Access Control without killing a single enemy