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