Short & Sweet Solution
Alright. First off, DO NOT ATTEMPT THIS ON YOUR FIRST RUN. I do not believe it possible, since you are limited for time. You are given 1.5 hours of real time to complete the entire campaign, AND do all of the princess wasp challenges.
NOTE: Doing the princess wasp challenges increase your characters powers, so doing as many of them before you do the missions makes it a little easier. Also, the collectibles and other trials rank up your character as well, and these are permanent.
So - use your first run on normal to work on collectibles and practise for your Friday Run.
When you leave the first safe house, go left and complete the first challenge. Easy. Then jump over the truck and complete the next. THen run and complete the next.
Now, remember IF YOU DIE you are sent back to the last check point. And honestly, you need all the time you have.
Now to be clear - you have 1.5 hours to get to the lab. Once you are in the lab, the timer stops. So don't worry. Outside you will have 1 fight, followed by 3 fights. There is a check point after the 1, but if you die at any of the 3 solider fights outside, you are put back at the start of the 3 fights - so go after the larger one at the front games first.
JUMP TO DISARM from afar all the super soldiers. They will kill you with ONE HIT.
After the 3 fights outside, you get a checkpoint before moving on inside. 1 more fight at the front door, and another down stairs. YOU MUST FIGHT THESE to trigger a cinematic to enter the final chamber.
Good luck. Time is not on your side here!