Here is the full list of all 19 Big Crown: Showdown achievements.
Purchase your first hat
Purchase all of the hats
Collect your first coin
Join a custom game
Knock 1000 objects off the track
Get your first knock-out
Be the last one alive but don't cross the finishing line
Complete a Local Multiplayer match
Complete an Online Multiplayer match
Make a custom game
Run a Marathon (26.2 miles)
Complete a round without punching
Play with 4 people locally
Complete your first game
Play with 4 people online
Collect all of the coins from a treasure chest
Get your first shield deflection knock-out
Knock the Knight's TV into the portal
Win your first game