Here is the full list of all 50 Star Wars the Clone Wars: Republic Heroes trophies - there are 36 bronze, 11 silver, 2 gold and 1 platinum.
Collect all trophies
Defeat Kul Teska on Behpour without either player dying
Finish all missions with another Player
Destroy 100 droids your partner has stunned
Finish a mission in co-op with a combined score of over 10000 points
Finish a mission with another Player
Get a Gold Medal for every mission
Get a combined best time for all missions under 200 minutes
Destroy 25 Droids by doing a jump attack off another character
Collect 50 Artifacts
Finish all Act 2 Missions on Master Difficulty
Finish all Jedi missions as Anakin & Ahsoka
Finish all Jedi Missions as Ahsoka
Get a Gold Medal for every challenge
Finish all Clone Missions as Cad Bane
Finish all Act 3 Missions on Master Difficulty
Finish all Act 1 Missions on Master Difficulty
Destroy 5000 droids
Get over 100 points while controlling each type of Droid
Destroy at least one droid with each Droid-Jak
Finish all Act 3 Missions on Padawan Difficulty
Get at least a Bronze Medal for every challenge
Destroy 10 Droids with a rolling Destroyer
Force Kill one of each type of Gold Droid
Destroy 20 droids with explosive props
Finish all Act 2 Missions on on Padawan Difficulty
Get a total score of over 200,000 points
Collect 25 Artifacts
Destroy 50 Droids with a mounted Force Kill
Buy every Hat & Mask
Buy all Droid-Jak upgrades
Destroy 50 droids with a clone melee attack
Destroy over 100 droids with Droid-Jaks
Destroy 25 droids while they are dancing
Finish all Act 1 Missions on Padawan Difficulty
Get a Platinum Medal on a Clone Mission
Push 50 enemies off an edge to their doom
Buy all Droid Dancing upgrades
Buy all Combat upgrades
Destroy 25 Droids by Jumping from Droid to Droid
Get over 250 points while controlling a single droid
Perform a Droid-Jak at the same time as your partner
Get a Gold Medal on a Clone Mission
Destroy a Gold Droid
Destroy 10 Droids attacking your partner
Collect an Artifact
Buy a Hat or Mask
Get a Platinum Medal on a Jedi Mission
Get a Gold Medal on a Jedi Mission
Finish the Prologue Mission: Master & Padawan