Here is the full list of all 31 Slime Rancher trophies - there are 14 bronze, 10 silver, 6 gold and 1 platinum.
Platinum
Reach at least 75,000 newbucks in Rush Mode
Obtain at least 3 gold plorts from a single gold slime
Score 50 points in a single game of slimeball
Place a tarr on the #1 Slime Stage
Fabricate 35 Slime Science gadgets
Fabricate your first Slime Science gadget
Have at least 10 types of largos on the Ranch
Complete Adventure Mode and set out for what's next.
Start bringing life back to the Glass Desert
Stand inside a rad aura for at least 15 seconds
Have 3 different veggie gardens on the Ranch at the same time
Have 3 different fruit trees on the Ranch at the same time
Incinerate an elder chicken
Feed 100 chickens to slimes on the Ranch
Fulfill a Range Exchange request between Noon and 2 PM
Have at least 3 different types of largos in the same corral
Use chroma packs to change the color of the ranch house, tech, and vacpack
Earn over 25,000 newbucks
Sell 500 plorts at the Plort Market
Earn 5,000 newbucks in a single day
Join the 7Zee Rewards Club
Shoot a boom slime largo into the air that explodes before landing
Constrain more than 15 slimes in your vac stream at once while on the range
Return to the Ranch after more than 24 hours
Stay awake from 6 AM to 6 AM the next day
Let a tabby slime headbutt you right on the nose
Jump into a corral containing at least 40 slimes
Burst a gordo slime
Send an adorable chick to a fiery end, the same place you're now destined to go
Shoot food into an airborne slime's mouth