Here is the full list of all 46 Lion Quest achievements.
Found 1 Gem
Achieved a top three high score in Lion Quest Arcade (beginner)
Unlocked Brendon the Cat
Found 1 Key
Unlocked Mildred the Owl
Cleared Level 1–9 as Jethro the Lion
Unlocked Tracy the Elephant
Cleared Level X3 – Patience
Cleared Level X2 – Turbine
Cleared Level X1 – Gauntlet
Cleared Level 8 – Secret Lagoon
Cleared Level 6 – Tidal Station
Unlocked Ronald the Bear
Cleared Level 5 – Zen Garden
Cleared Level 4 – Outer Space
Cleared Level 7 – Skull Island
Unlocked Jefferson the Fox
Cleared Level 3 – County Fair
Cleared beginner mode in Lion Quest Arcade
Played a game of Lion Quest VS against the A.I.
Played 10 games of competitive Lion Quest VS multiplayer
Cleared Level 2 – Red Cube
Cleared Level 1 – Shooting Rockets
Unlocked Leslie the Tiger
Unlocked Roy the Pig
Unlocked Wordsworth the Panda
Found all Keys
Found all Gems
Cleared Level 1–9 as Jefferson the Fox
Cleared Level 1–9 as Ronald the Bear
Cleared Level 1–9 as Tracy the Elephant
Cleared Level 1–9 as Brendon the Cat
Cleared Level 1–9 as Mildred the Owl
Cleared Level 1–9 as Leslie the Tiger
Cleared Level 1–9 as Roy the Pig
Cleared Level 1–9 as Wordsworth the Panda
Every item in the Lion Quest gift shop is sold out
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Played 50 games of competitive Lion Quest VS multiplayer
Played Lion Quest VS on all of the multiplayer maps
Cleared intermediate mode in Lion Quest Arcade
Cleared advanced mode in Lion Quest Arcade
Cleared expert mode in Lion Quest Arcade
Achieved a top three high score in Lion Quest Arcade (intermediate)
Achieved a top three high score in Lion Quest Arcade (expert))