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