Here is the full list of all 35 Battle Royale Tycoon achievements.
Entertain 1000 Guests
Build Arena Duel
Entertain a VIP
Complete Scenario 1
Complete Scenario 2
Complete Scenario 3
Entertain 5 VIPs
100 Guests in Park
500 Guests Visited Total
Unlock all Research
Build all Fun Buildings
Build Arena Defuse
Build Arena Team Deathmatch
Build Arena Capture The Flag
Build Arena King of the Hill
Build Arena Battle Royale
Use a Steam Workshop item
Buy 100 Weapons
Place 50 Environment Objects
Achieve Park Rating 60
Achieve Park Rating 90
VIP left with 80 Happiness
Hire 50 Workers
$100,000 in the Bank
Receive $500,000
Build ATM
Clean Up 100 Trash
Play 100 Months
Entertain Mr America
Entertain Blueprint Man
Entertain the Spartan
Entertain TF2 Medic
Entertain Spandex Man
Entertain the Ogre
Build Every Arena Type