Here is the full list of all 53 Euclidean Skies achievements.
Finish in 3 steps
Take only 1 step
Finish with one step
Take only 3 steps
Block enemy with dragon
Take only one step
Finish in under 5 steps
Unlock the other portal
Take fewer than 4 steps
Take 3 steps or fewer
Attack 2x with sword
Attack using sword
Take 4 steps or fewer
Take fewer than 8 steps
Take 5 steps or fewer
Take fewer than 20 steps
Take fewer than 9 steps
Take fewer than 5 steps
Take fewer than 7 steps
Take fewer than 6 steps
Arrange all cubes into two horizontal layers
Don't panic
Take fewer than 25 steps
Defeat all enemies
Beat the boss
Take 2 steps or fewer
Take 7 steps or fewer
Take 8 steps or fewer
Take 20 steps or fewer
Take 13 steps or fewer
Take 12 steps or fewer