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