Here is the full list of all 51 Livelock trophies - there are 43 bronze, 4 silver, 3 gold and 1 platinum.
Unlock all Trophies
Complete a COOP Mission with 3 players using Hex, Catalyst and Vanguard
Reach level 30 with Hex, Catalyst and Vanguard
Reach Level 30 with Hex
Reach Level 20 with Hex
Survive 15 minutes in Survival OP Mission
Survive 10 minutes in Survival OP Mission
Survive 5 minutes in Survival OP Mission
Collect all Hex Audiologs
Collect all Audiologs
Decrypt all Master Data Cards
Reach Level 10 with Hex
Reach Level 30 with Vanguard
Destroy 10000 enemies
Reach Level 20 with Vanguard
Collect all Vanguard Audiologs
Reach Level 10 with Vanguard
Reach Level 30 with Catalyst
Complete all missions on Hard
Complete all missions on Medium
Complete all missions on Easy
Complete ACT 03
Collect 2500 Carbon
Collect all Catalyst Audiologs
Collect all Story Audiologs
Decrypt all Data Cards
Destroy 100 Upgraded enemies
Complete ACT 02
Reach Level 20 with Catalyst
100 Destruction streak
Complete ACT 01
Have a Helmet, Cape and Alloy equipped at the same time
Equip first Cape
Complete a COOP Mission with 3 players using 3 of the same class
Reach Level 10 with Catalyst
Destroy 1000 enemies
Complete a COOP Mission with 3 players.
Complete a COOP Mission on Singular Difficulty without Reprinting
Decrypt a Master Data Card
Equip first Alloy
Collect 500 Carbon
Destroy 10 Upgraded enemies
Equip first Helmet
30 Destruction streak
20 Destruction streak
Destroy 100 enemies
Collect 100 Carbon
Destroy 1 Upgraded enemy
Collect an Audiolog
5 Destruction streak
Decrypt a Data Card