Here is the full list of all 44 The Persistence Enhanced trophies - there are 32 bronze, 7 silver, 4 gold and 1 platinum.
Collect all trophies
Enter Research Deck after the tutorial
Plot the jump vectors home on Research Deck
Refuel the Stardrive
Repair the Sensors on Communications Deck
Find the Captain's body on Engineering Deck
Complete the game
Save both Serena and Zimri
Open 25 supply crates
Make any schematic
Make an epic schematic
Make an Epic of each suit, teleporter, shield, harvester and supersense
Unlock a weapon
Unlock all weapons
Upgrade a weapon
Get any weapon to Max level
Upgrade any DNA stat
Upgrade each DNA stat at least once
Get all DNA stats to max
Kill 100 enemies by harvesting their stemcells
Shoot and kill 6 enemies in a row, with just 6 bullets
10 headshots in a row
Kill 3 enemies with the same gravity bomb
Kill 5 enemies with the same Swarm Droid
Smash an enemy to death with the Gravimetric Hook
Pin two enemies with the same Valkyrie bolt
Melee kill a Berserker with the Stem Cell Harvester
Have a single Ivy Serum buddy kill 5 enemies
Power up any Debris Defence Shield machine
Power up all the Debris Defence Shield machines
Use all 4 Debris Defence Shield machines on the same life
Find a crew member artefact
Find all 6 crew member artefacts
Print a clone of any other crew member
Print a clone of all 7 crew members
Kill one of each type of enemy
Use the environment to kill 10 enemies
Rage Berserkers to kill 10 enemies
Get a weeper to kill another mutant (without using Ivy Serum)
Kill any enemy with a hidden Siren Grenade
Use your shield 10 times against the same enemy
Get fireballs to kill a total of 10 mutants
Visit Research and then Stardrive decks on any one life, without walking
Visit all 4 Decks on any 1 life, without collecting anything or making a weapon