To unlock the Battle Tested trophy in Call of Duty: Black Ops 4, you simply need to reach level 55 (Commander) in Multiplayer.
Generally speaking you want to select the game modes which have objectives and make sure to go for those objectives in order to earn more XP. Domination and Search & Destroy are good examples.
If you go to the Options menu in the Multiplayer menu, you can tab over to Challenges and see what you can work towards. Challenges span over multiple multiplayer sessions so you can keep making progress towards big XP bumps. Complete a full set for 5000XP.
Once you hit level 55 this trophy will unlock.