Toward the end of Mission 7: Federation Day, after you turn off the elevators to stop enemy forces from closing in on your position, you will rappel down a building for the 3rd time. Once you interact with the rope, just wait for a couple of seconds and don't do anything. The photocopier will fall right on your face, unlocking the "Carbon Faceprint" trophy/achievement.
Near the end of Mission 10: Clockwork you must escape an enemy facility. While your teammate is driving you will be using a grenade launcher turret. There will be plenty of vehicles chasing you. Instead of shooting at them directly, shoot just in front of them to blow a hole into the ground. If they drive over it, the vehicle and its crew will get knocked out, which counts towards this achievement/trophy. Do the same to 8 different vehicles before reaching the end of the mission to unlock the achievement/trophy.
"It Came From Below!"
There are three different locations in Mission 6: Legends Never Die where you can kill enemies while underwater. The water is only waist-deep so crouch, and then kill enemies with your knife. Do this on the "Rookie" difficulty to make it easier. Enemies will still be shooting at you when you go underwater, and you must get very close to them to perform knife kills. Simply run up to the enemies standing in water, crouch, and use the knife to kill them to unlock the achievement/trophy.
Play Mission 2: Brave New World and after taking out the enemies at the gas station, you will have to fight your way through an old sewer. Once you reach the end of this area, you will be attacked by two helicopters. The first (smaller) helicopter will eventually fly away, so take it down quickly. There are many MAAWS rocket launchers on some crates. Take one and, when shooting, keep aiming at your target to guide the missile. Shoot down both helicopters using the rocket launcher to unlock the achievement/trophy.
After you upload the virus in the server room on Mission 7: Federation Day, , you must rappel down the building. Kill the two enemies on a balcony first to avoid being detected. Two floors below that balcony is an enemy sleeping in a chair. Shoot him through the window to unlock the achievement/trophy.
In Mission 4: Struck Down you must use the remote sniper four times to progress in the mission. Only fire when your crosshairs turn yellow to make it a guaranteed hit. In the first sequence you must kill at least one enemy, and your team will do the rest. In the second sequence you must take out four enemies with rocket launchers. In the third sequence, you must clear an airfield, and kill several enemies. During the fourth sequence you have to kill the three enemies that fire their MGs from vehicles. If you miss a shot, just restart the checkpoint at any time. Even if you restart, you will still to unlock the achievement/trophy.
"Cog In The Machine"
At the start of Mission 13: End Of The Line, quietly kill the first five enemies by yourself, making sure you're not seen or heard. Kills from your teammates do not count. Use silenced weapons to remain undetected. The first kill will happen automatically when you jump down a ledge, the second enemy is in the train yard, and the third enemy is with three other enemies. Wait until your teammates arrive and shoot either one of the enemies. Your team will take out the rest. The fourth and fifth enemies are behind the gate that your teammate opens for you. Go prone and kill both of them quickly before your teammates take them out.
"David & Goliath"
Toward the middle of Mission 12: Into The Deep you must use a torpedo to destroy a warship. While guiding the torpedo, you will automatically be using thermal vision and can see a red area on the side of the ship. Hit this red area to destroy the LCS and unlock the achievement/trophy.
"End Of Your Rope"
At the start of Mission 15: All Or Northing you must clear the flight deck of enemies. Once done, you will have to pick up the Osprey targeting control. After you pick it up, enemies will start attacking the ship from the side. They will come in dinghies and throw grappling hooks on the ship. Wait until an enemy starts climbing the rope, then cut it with your knife to unlock the achievement/trophy.
Just after Mission 16: Severed Ties starts, you will see a prompt on the screen that says "Press TRIANGLE/Y to switch to guided rounds". When this occurs, attack helicopters will arrive. Just do as instructed and switch to guided rounds to shoot down all three helicopters and unlock the achievement/trophy.
Near the end of Mission 11: Atlas Falls you must use a console to regulate the pressure of some valves. It is part of the story and cannot be missed. There will be three bars on the screen. You need to keep them in the center, so they are colored green. Use the Left Analog-stick to move the bars up and down to keep them in the green zone. It doesn't matter if they drop to the yellow zone briefly, just as long as you bring them back to the green zone quick enough.
During Mission 14: Sin City, you will come upon an egyptian casino. Tons of enemies will ambush you in this area. Destroy every slot machine in this area by shooting their screens. At the end of the casino is a gate that one of your teammates will raise for you. Go under it, and you will reach a broken escalator. Before walking down the escalator, look to the opposite side of the room to find five more slot machines. Destroy their screens to unlock the achievement/trophy.
You have to complete Mission 9: The Hunted without ever being spotted by an enemy to get the "Jungle Ghosts". During the first part of the mission, you are on your own. Stay to the left side of the area, and watch the radar. Nearby enemies will be shown with red dots on the radar. You can kill any necessary enemies. Remain crouched to avoid being noticed. While in the second area, you will see some burning rubble. Move slowly, and stay to the left side again until you reach your team. From this point on, you will only need to follow your teammates and do exactly what they say. If you are spotted at any point, just restart the checkpoint, and try again.
"Piece Of Cake"
While playing Mission 11: Atlas Falls on the Veteran difficulty and after using the grapnel gun, you will have to kill tons of enemies and go to the common room. You must then breach the door. After the door has been breached, throw all your flashbangs and frag grenades to kill the enemies inside. Don't waste any grenades before reaching this room. If you do not kill all enemies with your grenades, you can simply let your teammates kill the rest of them. If you get hit at all, restart the checkpoint, and try again.
"They Look Like Ants"
Near the conclusion of Mission 17: Loki you will be controlling weapons from space. You can see the exact blast radius when aiming. The ammo is infinite so you can shoot as often as desired. Kill the foot soldiers first before destroying the main targets. Make sure to carefully kill all enemies before destroying the final target. Do not aim anywhere near the allies or they will die. If you think you may have accidentally killed allies, simply restart the checkpoint, and try again.
After killing the first enemies in Mission 18: The Ghost Killer you will be attacked by many helicopters. Just after this, the grapple guys will climb up the train. There are four of them, but you only need to kill two of them to get the "Tickets Please". You have to kill them before they reach the top of the train. If you fail to do this, restart the checkpoint, and try again.
In Extinction mode, first destroy all 12 hives to unlock the computer that initiates the exfiltration countdown. The computer will spawn near the final hive, and all players have to activate it simultaneously. From then you will have 2 minutes and 30 seconds to get back to the helicopter in the starting area. Meteorite barricades will block your way, but they will automatically fall apart after 30 seconds, and there are only two of them. You will also be attacked by several heavily armored Rhinos, so use armor breaking ammo to kill them. Fully upgraded sentry guns are recommended, as they distract and damage the Rhinos. If your health gets low, deploy fully upgraded armor vests. Armor can be very useful if you are running and a Rhino attacks you from behind. Make sure all players have armor vests in their loadout to avoid going down.