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