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