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