Here is the full list of all 27 Arena Hero achievements.
Complete the bronze league.
Defeat a boss.
Discover 10 unique items.
Defeat a champion enemy.
Complete the chaotic bronze league.
Complete the silver league.
Complete the chaotic silver league.
Complete the gold league.
Complete the chaotic gold league.
Complete the champion's league.
Complete the chaotic champion's league.
Wear a tier 2 armor set.
Complete a chaotic arena.
Have 5 enhancers equipped.
Have 7 tier 3 items equipped.
Reach hero level 20.
Reach hero level 40.
Reach hero level 60.
Reach hero level 80.
Reach hero level 100.
Discover20 Unique items.
Discover 40 unique items.
Discover 60 unique items.
Discover 80 unique items.
Bounce 3 times off the air.
Defeat the slime king without attacking it.
Defeat a Legendary enemy.