Here is the full list of all 46 Beach Buggy Racing trophies - there are 34 bronze, 8 silver, 3 gold and 1 platinum.
Drive 1000km
Earn all the stars in Tropical Twist
Recruit 5 drivers
Smash 50 death bats
Smash 20 lava monsters
Smash 100 seagulls
Win a 1000hp Race without resetting
Win a 1000hp Race without using the brake
Win with a chicken on your face
Bounce off three different turtles in one river crossing in Dino Jungle
Earn all the stars in Chowder Bowl
Jump 400 meters
Successfully complete the triple-jump shortcut in Death Bat Alley
Knock the Tiki Temple's teeth out
Smash 40 crabs
Smash 100 penguins
Knock the penguin off the mammoth tusk in Glacier Gulch
Beat 7 Daily Challenges in a row
Do a jump start
Find 1 Easter Egg
Set fire to an opponent who's frozen
Earn all the stars in Sunshine Sprint
Beat a Daily Challenge event
Drive 100km
Take out three drivers with one Death Bat Powerup
Earn all the stars in Coconut Cup
Go from last to first place on the last lap of a Race
Paint a car
Earn all the stars in Easy Street
Win a Race without using a Powerup
All Trophies
Earn all the stars in Pineapple Punch
Earn all the stars in Tidal Rush
Earn all the stars in Typhoon Trophy
Drive 9,289km
Earn over 1,000,000 coins in your career
Smash 500 palm trees
Smash 25 yeti
Find 10 Easter Eggs
Score 25 in a Follow the Leader event
Use Remote Control to detonate a car under the Nitro effect
Use Earth Strike on an opponent who's experiencing Low Gravity
Freeze an opponent who's on fire
Use B'Zorp to teleport into 1st place within 100m of the finish line
Win one 1000 HP Championship
Win five 1000 HP Championships