Here is the full list of all 48 Start the Party! trophies - there are 32 bronze, 13 silver, 2 gold and 1 platinum.
Pop a colour chain of 70+ fish in Poppin' on Hard difficulty
Find the 5 bugs in less than 5 seconds
Play 20 games of Survival
Play all the Party Games, on all difficulties in Free Play
Zap 15+ robots in one game
Get the bonus item in every Party game
Play all the Party Games in Free Play
Swat 50 bugs in one game
Get every bonus object within a single Party Mode play session
Shoot down 6 ghosts on their way to scaring you
Earn 20 stars in a single Party session
Catch 10 pizza toppings in one game, during a Three Strikes round
Rescue 3 people just before the monster eats them
Use 5 litres of paint within the templates in one game
Sshhh, don't disturb the chick!
Save 30+ chicks in one game
Play a game of Start the Party!™ (any game mode) on Christmas Day
Play a game of Start the Party!™ (any game mode) between 12 o'clock and 1 o'clock at night
Smash a Piñata in less than 5 seconds
Earn 15 stars in a single Party session
Munch 5 bugs in one game
One player wins 3 rounds in a row in Party Mode
Steal the last star from someone in the Robber Round, reducing their star count to 0
Re-record someone's name
View the credits
Get to the top of the leader board in Survival Mode
Hit 8 moles in a single game
Surrender to 8 angry mobsters
Survive for 2 minutes
Match 5 characters in one game
Survive for 1 minute 30 seconds
Survive for 1 minute
Survive for 30 seconds
Steal enough stars in the Robber Round to get from last to first place
Steal 5 stars in one turn in the Robber Round
Draw on a player’s face
Completely smash a rock in less than 3 seconds
Clean all the crocodile's teeth
Waft 12 paratroopers to safety
Use 5 litres of hair dye in one game
Pop a colour chain of 20+ fish
Collect all other trophies for Start the Party!™
Play 10 games of Party Mode
Take 100 different player portrait photos
Play all the games in Start the Party!™
Survive 20 seconds with a perfect lolly
Bounce an object 10 times without dropping it, during a Three Strikes round
Slice 40 pieces of fruit during a Three Strikes Round