Here is the full list of all 24 Tunche: Arena achievements.
Annoy the Skill Tree guy
Defeat Boutu in Horde mode.
Reach S combo style.
Air juggle the frog plushie 5 times.
Choose a reward in Horde mode.
Access any of the Leaderboards.
Buy a skill in Endless mode.
Defeat one enemy of each type.
Complete a Wave in Endless mode.
Defeat Boutu in Horde mode without being damaged.
Defeat 200 frogs in total.
Defeat 75 monkeys in total.
Defeat 30 trunks in total.
Defeat 50 peccaries in total.
Defeat 10 giant frogs in total.
Reach Wave 50 in Endless mode.
Get a total of 50 S, SS or SSS kills in Endless mode.
Beat Horde mode without having chosen any reward.
Beat Horde mode without having spent XP on the Skill Tree.
Reach SS combo style.
Reach SSS combo style.
Use all the skills.
Clear a Wave without getting hit.