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