All the "max out" trophies should be the last ones you work on. Reason being, when going for solo, co op, or HVTs, you'll build xp for all of those missions, so you may level some characters up during your attempts to get the other trophies.
If you don't mind a grind, the fastest mission in this game is 02, Ranked mode. Even faster if you can get a co op buddy to join an online game for the 2nd mission.
Here's the layout of mission 02:
From the start, head into the empty hallway on your left, just to hide in here for a moment, while the enemy up the stairs ahead heads out of his room. That's your time to strike him in the head when he's not looking. Just past him is the intel, so grab it and head back to where you spawned and go down the corridor instead. At the end of it, just before it leads outside, is a sensor trap. Take it out with a silenced pistol. After you do that, take cover at the corner and watch the enemies in the courtyard. One should be walking away furthest left, and 2 should be talking, but ending their convo at this point. When they do, they'll walk towards the left, turning the backs at you mostly. Sneak past them to the right (there are stairs) and up the stairs you'll see an enemy walking away from the stairs. Knife him in the back and steal the intel just past him. At this point, if you know where to go, you can run.
Quickly do a 180 and go back down the stairs you just came up from. Head immediately to the left and then to the right, which takes you back to spawn. The exit door is exactly where you spawned in on this map.
If you don't want to grind this, simply play through the game, or play co op, or even dynamic missions. Everything gives you xp, so just keep playing.