Here is the full list of all 28 Hexahedra achievements.
Complete Going Solo using only one command track.
Complete Another Fine Mess without using a Panel Sensor
Complete the second order for the galaxy's ugliest cubes
Complete Colour Sorting in 150 steps or fewer
Ship the remains of Kickstarter backers to their final resting place
Complete Rest In Panels without using any Spray Painters
Get a new job
Complete a work order for the GHSI inspector
Side with Juliana and take over the galaxy
Side with Dantar and the inspector and stop Hexahedra Inc.
Fire a Laser through a glass panel
Have two lasers trigger each other
Repair a metal or wooden panel
Add a payload to a cube
Teleport a cube into and out of the Teleport Buffer
Reflect a laser beam from a Coloured Panel after repainting it with a Drop Painter
Burn five wooden panels from a cube containing a payload in a single step, without failing the level
Find the engagement gift
Break or equal the Devices record for any non-tutorial Campaign level, after level 10
Break or equal the Steps record for any non-tutorial Campaign level, after level 10
Break or equal the Commands record for any non-tutorial Campaign level, after level 10
Find Octavius in his wizard hat and complete his work order
Find Octavius in his funky hat and complete his work order
Find Octavius in his sailor hat and complete his work order
Find Octavius in his propeller hat and complete his work order
Complete all of Octavius's jobs
Create and solve a custom puzzle
Download and solve a puzzle from the Steam Workshop