Here is the full list of all 51 Syndicate trophies - there are 46 bronze, 4 gold and 1 platinum.
Platinum
Achieve a perfect result in all the Tutorial challenges
Breach 873 grenades
Breach an entire barrage of five missiles in the Ramon boss fight, on normal or hard difficulty
Kill an enemy from the explosion of a reactive armor unit.
Defeat Tatsuo without restocking your ammunition from the UAVs, on normal or hard difficulty
Kill 3 or more enemies from the electricity discharge of a dying electro armor unit
Kill Agent Crane before you kill his two sidekicks, on normal or hard difficulty
100% completion (level, research and challenges)
Kill 4 enemies in 4 different ways within 1 minute
Use a penetration weapon to kill 500 enemies through cover, while in DART Overlay
Defeat Kris without making him visible using EMP or DART Overlay, on normal or hard difficulty
Kill 50 enemies with all the weapons in the game
Achieve CEO ranking on all combat levels on hard difficulty
Make it past the conveyor belt without taking any damage from the turret
Defeat the final boss without allowing any agent to be revived, on normal or hard difficulty
Successfully sprint tackle 25 riot shield units
Find all propaganda tags (unlock all propaganda tag infobank entries)
Complete all chapters which track difficulty, on hard difficulty
Unlock the Datacore in the minimum number of breaches
Find all business cards (unlock all the business card infobank entries)
Don't kill any EuroCorp civilians with the minigun in chapter 8
Complete the game on any difficulty (given at the end of Datacore)
Kill enemy soldiers of two different syndicates fast enough to receive a rampage energy bonus
Complete chapters 12, 13, 14 and 15 on normal or hard difficulty
Kill 3 specters in chapter 14 without using EMP effects on them, on normal or hard difficulty
Complete all Co-Op maps on expert difficulty
Do 250 rampage kills/kill streaks
Collect 500,000 energy
Use breach abilities 300 times
Get the rampage bonus up to 5 sequential kills
50% completion (level, research and challenges)
Complete chapters 10 and 11 on normal or hard difficulty
Score a 2,000 points combo
Complete all Co-Op maps on any difficulty
Use the Swarm's multi-target lock-on firing mode to kill 3 UAV drones with one volley
Complete chapters 7 and 8 on normal or hard difficulty
Complete 10 Contracts against members of your syndicate
Save a team member that is stunned by an electron mace
Complete a mission without going down
Kill 50 enemies with melee executions
Heal 3 team members for at least 50% of their health within 1 minute
Do 10,000 points of damage to enemies and heal or block 10,000 points of damage on team members using applications
Defeat an enemy agent squad
Finish your first research
Be a member of a Syndicate consisting of at least 4 people
Complete a mission after earning a team savior score
Complete chapters 2, 3, 4 and 5 on normal or hard difficulty
Obtain a health bonus from network connect links from your upgrade choices (single player only)
Achieve CEO ranking on any level
Complete Wakeup Call