Here is the full list of all 15 Rising Islands achievements.
First relic recovered
Used a spring jump
First powercrystal recovered
Experienced failure
First collectible crystal found
Ran on a wall
Completed the tutorial
Completed the game
Finished a time trial level
Do a grind
Learned to dash
Second relic recovered
Third relic recovered
Found all collectible crystals in a level
Found all collectibles in the game