Follow the indicated walkthrough for the listed codex entry (challenge) to complete it. Complete all 52 codex entries (challenges) in the campaign to get the "Master Of Adaptation" achievement/trophy. The codex entries also unlock new multiplayer modifications, like weapon mods. During an active mission, you can pause the game to view the available codex entries and their objectives.
German Anti-Tank Tactics (Field Gun Locations)
While attempting this codex entry in the "Over The Top" mission, you should not die or restart checkpoints. Sometimes when you restart a checkpoint one of the field guns will disappear and you cannot destroy it again. If that happens you will not be able to complete the challenge in your current playthrough and have to restart the mission. Make sure each field gun does explode. Shoot it a few times if you are unsure. There are a total of 36 you must destroy to complete the codex entry.
Booby Traps (Kill 2 Enemies with Tripwire Bombs)
During the "Fall From Grace" mission, collect a tripwire bomb from one of the weapon boxes. One can be found at the very beginning. There is a truck driving along the road to your left when the mission begins. Follow that road. On the right side of the road by some sandbags is a weapon box with the tripwire. Run up to a group of enemies and put all tripwires on the ground in front of them. Wait for them to walk into it. If there are enough enemies close together, you should easily get 2+ kills.
Airborne Cannons (Destroy 10 Aircraft in 30 Seconds)
At the end of the "Forte Et Fidele" mission, you will mount an anti-air cannon. You must shoot down 10 enemy planes very quickly. Friendly planes cannot be shot down. Enemy planes have a red color and will show up on the radar. It is recommended that you increase the aim sensitivity so you can aim faster. There is a group of four planes at the start coming straight at you. Then, shoot down a few more to your right and in front of you. Another swarm of three slow planes will show up behind a cloud on the right. Shoot down all of them quickly. At this point you should have 10 kills -- otherwise try getting a few more. Time is very short on this and there are not a lot of enemy planes (many of them are friendly teammates that cannot be shot down). This is the hardest challenge in the game and will take a few attempts. Simply restart the checkpoint and try again until you complete it.
Geology (5 Kills with Rifle Grenades)
During "The Runner" mission, you must collect the Rifle Grenade (a type of grenade launcher) from weapon boxes. There are two of them. One to the right at the starting point and another one in the building that is marked as a main objective. Each of these has three shots. To kill five enemies, you will likely have to get both of them to have enough ammo. Shoot the grenades close to enemies to get a total of five kills with this weapon.
Drip Gun (10 Sidearm Kills)
During "The Runner" mission, you must collect the Howdah Pistol from a weapon box. It can be found behind a building to the far left of the starting point (on the hill near the main objective). Kill 10 enemies with this pistol to complete the codex entry.
Desert Cars (Destroy Vehicles Unseen)
During the "Hear The Desert" mission, collect the dynamite from the tent to the right of the starting location. Then, sneak up to each car and throw dynamite near it, but do not blow it up yet. Once you have placed dynamite at each car, blow up all three at the same time. If you blow up the cars one by one, the enemies may turn hostile and hunt you down.