Here is the full list of all 44 Super Puzzle Platformer Deluxe achievements.
Completed the Glass Splitters challenge
Completed the icicles challenge
Completed the flail challenge
Completed the TNT II challenge
Got to power level 4 in War of the Woods
Unlocked Rocket Launcher (Collected 500 block bits in a single life)
Got to power level 4 in Mansion Mania
100 Jewels Collected
Got to power level 4 in Icy Island
Completed the TNT challenge
Completed the Tower Down challenge
Completed the chainsaw challenge
Completed the drill challenge
Completed the Tower Up challenge
Completed the spikes challenge
Got to power level 4 in Cookin' Caves
Unlocked Fighter outfit (Collected 3 stars in a single life)
Got to power level 4 in Retro Relic
Unlocked Jetpack (collected 3 jewels in a single life)
Unlocked Duel Wield outfit (Collected 6 jewels in a single life)
Got to power level 4 in Troublesome Tech
Unlock Ninja outfit (collected 100 block bits in a single life)
Survive 10 minutes in a single life
Unlocked Cyborg outfit (Collected 10 stars in one life)
Unlocked Beezleblock outfit (Defeated Beezleblock)
Completed the cannon challenge
Completed the cannon II challenge
Completed the fireball challenge
Completed the fireball II challenge
Completed the firespinner challenge
Completed the homing missle challenge
Completed the flail II challenge
Defeated Beezleblock
100 percent complete
Die 1000 times
120 percent complete