Here is the full list of all 42 Starlink: Battle for Atlas trophies - there are 25 bronze, 13 silver, 3 gold and 1 platinum.
Destroy a Dreadnought
Acquire a Legendary Mod
Earn 3 skill points from mastering ships
Gain 100% alliance on a planet
Map every part of a planet
Use Fusion to craft a higher-level mod
Discover your first new planet outside the Trade Sector
Destroy A Prime
Use Heat to defeat an Ice Giant
Defeat 10 targets by shooting at their weak spots using Precision weapons like Shredder
Build 8 Equinox Upgrades
Thermal Shock 10 targets
Time Active Shield perfectly to reflect an attack 10 times
Shatter 5 Frozen targets
Use Cold to defeat a Fire Giant
Trap 3 targets in a single Gravity Vortex
Enter space from a planet for the first time
Equip your first mod
Earn all Trophies
Extend Starlink's range to bring the fight to Grax
Defeat Grax
Build a Starlink Tower on every planet
Loot 10 derelict ships in space
Neutralize 5 Outlaw Hideouts in Space
Find a Warden Relic
Equip 8 ship & weapon mods on a ship build, using Rare, Epic, or Legendary mods
Fill your ship with Epic or Legendary Mods
Discover all the planets in Atlas
Record every Discovery on a planet
Discover 5 Animal Species
Discover every animal species in Atlas
Defeat an Extractor or Prime with your shields down
Hit 5 targets with a single Stasis blast combo
In COOP, repair your partner after they get shot down
In COOP, defeat a Prime together
Build your first Expedition workshop
Ally with all 5 Outpost types
Get at least 25% alliance on every planet
Earn 6 Pilot Skill points from mastering weapons
Invest in a pilot's Mentor skill, to make your whole crew stronger
Spend 14 Skill Points on a single pilot
Upgrade two sections of the Equinox to their maximum level