Here is the full list of all 35 Octahedron: Transfixed Edition achievements.
In 3-1: Trap 4 enemies in the box-shaped area you start the level in
Beat 2-1, destroy all breakable floors
Find the hidden shortcut in 2-4
Beat X4-4 using only the basic platform
Finish the game
Beat World 5
Get all optional upgrades
Beat 5-T and collect all of its tetrahedrons
Beat World 4
Beat World 3
Beat World 2
Beat World 1
Begin your journey (beat the intro stage)
Collect all tetrahedrons
Get all 100% Medals
Get all Deus Medals
Get all Par Any% Medals
Get all Par 100% Medals
Beat 3-1, destroy no light bulbs or enemies, collect nothing
Beat X2-2 while touching the ground just once
Beat X4-1 while touching the ground just once
Beat World 1 in Rogue Extra mode
Get all Time Medals
In 2-5: Block 5 projectiles using your platforms, without touching the ground
Beat 2-7, destroy all light bulbs, but don't collect any flowers
Beat 4-1, don't kill any bees, don't touch any beehives, don't lose a life
Beat 3-8, destroy no light bulbs or enemies, collect nothing
Beat 3-9, destroy no light bulbs or enemies, collect nothing
Beat 4-4, destroy no light bulbs or enemies, collect nothing
Beat 1-6, collect and destroy nothing, don't get detected by a scanner, don't get hit
Beat 4-7, collect and destroy nothing, don't get detected by a scanner, don't get hit
Beat 3-5 while touching the ground just twice
Beat X3-4 using only the basic platform
After unlocking all optional upgrades, revisit 1-2 to get a Par Any% and a Par 100% Medal at the same time
Beat the game in under 2 hours