Here is the full list of all 50 Adventure of Leek achievements.
Complete Speedrun Mode in less than 10 minutes
Attempt Speedrun Mode
Beat Worm Caves II (Without Dying)
Defeat 100 skull things
Lose 100 Lives
Defeat 100 snails
Beat Lava Land I (Without Dying)
Defeat 100 worms
Beat Canyons II (Without Dying)
Look through the credits
Beat Lava Land III (Without Dying)
Beat The Game
Defeat Plum
Collect All The Coins (Lava Land III)
Beat Worm Caves III (Without Dying)
Throw 1000 Water Balloons
Beat Canyons I (Without Dying)
Run out of Lives
Beat Lava Land III
Beat Lava Land II (Without Dying)
Beat Lava Land II
Collect All The Coins (Lava Land II)
Beat Lava Land I
Collect All The Coins (Lava Land I)
Defeat 10 skull things
Defeat 10 worms
Defeat The Serpent
Enter Lava Land
Beat Worm Caves III
Collect All The Coins (Worm Caves III)
Throw 100 Water Balloons
Beat Worm Caves II
Beat Worm Caves I (Without Dying)
Collect All The Coins (Worm Caves II)
Lose 10 lives
Beat Worm Caves I
Collect All The Coins (Worm Caves I)
Beat Canyons III (Without Dying)
Defeat The Moquito Brothers
Enter The Worm Caves
Beat Canyons III
Collect All The Coins (Canyons III)
Beat Canyons II
Collect All The Coins (Canyons II)
Beat Canyons I
Collect All The Coins (Canyons I)
Defeat 10 snails
Throw 10 Water Balloons
Lose 1 life
Enter The Canyons