Here is the full list of all 24 Froggo Swing 'n Grapple achievements.
Complete a stage without taking damage
Complete a stage without triggering a single checkpoint
Complete the game without dying once
Sleep on the mushroom bed
Unlock a secret version of a stage
Complete all rain levels
Save yourself from falling into a pit
Purchase shoes from a shoes shop
The super secret technique
Complete the first half of the game
Complete a room without leaving the ground over once
Complete the game
Defeat Lime King
Defeat Soul Snake
Defeat enraged Umbrella Knight
Skip enraged Umbrella Knight
Progress without disturbing Lily
Win the second fight with Grappler Knight without the Grappling extender
Bring Umbrella Knight to the end of a stage
Collect 1000 coins
Collect 10000 coins
Collect all of the gems from every stage
100% Complete a save file
Eat 50 bugs