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