Not mine, the credit goes to: The Pants Party, Eternal
It would obviously save you time to do all these at the same time by starting on Legendary, since the achievements stack. Going through on co-op with 3-4 people makes this extremely easy and shouldn't take you more than eight hours or so. Here are some general tips:
* Make good use of checkpoints. If you need to, run around and die once to get a feel for where the enemies are and what course of action you need to take.
* Be cautious once you know what to expect. Take it one enemy at a time if you can. Make good use of your grenades. If you have plasma or brute grenades, try to get a stick on one of the bigger enemies to take them right away. Some may require two, but it's much faster than picking away with a battle rifle.
* Let your NPCs do some work for you. They're not exactly powerhouses and you can't let them do everything, or they'll just run out and get killed, but they can lay down some initial fire and draw the enemies to them, then you can pop out and get more shots off without taking damage.
* Your shield recharges, make use of it. If you get hit once, more are sure to follow, so find some cover and recharge. The enemies will usually watch the area you went into cover, so if you can sneak around to another side from there, you can probably catch them off guard.
Note #1: The level achievements must be done in one go through or it won't register the achievements. In other words, don't save and quit in the middle of a level, wait until the start of the next level.
Note #2: You can not simply beat the last level on Legendary to get the achievements, each one has to be done. You can do some on co-op and some solo and it still works, just check that there is a shield in the bottom right corner when you highlight a level. You must even watch the opening cutscene on the same difficulty to unlock the Campaign Complete achievements.