Here is the full list of all 52 Adventure Rush achievements.
Get a U.F.O
Buy 100 Items
Destroy 1000 Boxes
Get a Hourglass
Get a Pixie
Collect 10000 Gold
Destroy 500 Boxes
Eat 1000 Foods
Hunt 5000 Creatures
Collect 5000 Gold
Get a Cullinary Book
Destroy 250 Boxes
Defeat the Dragon
Eat 500 Foods
Reach the Vulcan
Defeat the Lich
Reach the Mistery Woods
Defeat the Goblin Master
Reach the Goblin Camp
Defeat the Swamp Pillow
Get a Medicine Book
Eat 250 Foods
Destroy 100 Boxes
Boost your speed
Buy 10 Items
Collect 1000 Gold
Hunt 1000 Creatures
Reach the Swamp
Defeat the Chimera
Boost your Vitality
Reach the Village
Defeat the Yeti
Destroy 50 Boxes
Buy your first food
Reach the Snowfall
Defeat the Sand Worm
Eat 100 Foods
Hunt 500 Creatures
Reach the Desert
Defeat the Mother Spider
Eat 50 Foods
Reach the Spider Cave
Defeat the Beholder
Boost your power
Reach the Ruins
Defeat the Treant
Hunt 100 Creatures
Buy your first Weapon
Hunt 10 Creatures
Collect 1 Gold
Reach the Forest
Start a new adventure