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