Here is the full list of all 19 Axium's Box achievements.
You died
You Unlocked the portal
You set Carla free
You traveled one mile
You set Gideon free
Get all the fragments you can before you unlock higher jump
Get all the fragments you can before you help Carla
Get all the fragments you can before you help Gideon
Gather all 400 fragments
Defeat ???
Win On Insane difficulty
???
KILL
Help the strange lady
Help the edgy teen
Get all the fragments you can before you help the edgy teen
Get all the fragments you can before you help the strange lady
Get all the fragments you can before you destroy the crystal