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