Here is the full list of all 11 Neon Arena achievements.
Get on a 15 kill streak!
Finish the Arena in Co-op mode
Blast 15 enemies with a single bomb
Burn 20 enemies using a flamethrower
Kill 25 enemies using a spreadgun
Get on a 35 kill streak!
Get all the 5 stars in primary game mode
Finish the Arena with at least 50% of spheres left!
Finish the Arena with at least 75% of spheres left!
Finish the Arena with all 100% of spheres
Finish the Arena with at least 3 lives left