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