Well, the safest methods I could devise, at least. I played this almost too carefully; nothing flashy here, but it worked well. Camping in corners where you can melee enemies through a wall if necessary is an effective strategy for many maps. Throwing objects and guns is also overpowered, so I used that a lot. Don't forget to slow motion jump when you're in a jam to dodge bullets, too. Most importantly, do not rush yourself whatsoever—there's no need, since time completely stops when you're not moving. Carefully consider your every action, and where the next red dudes will be spawning.
Was surprised to succeed on my very first attempt like this, but I guess beating the levels over a dozen times each during other challenges and modes prepared me fairly well, although I did have several close calls. Honestly, I think the real time speedrun challenge was harder than this one. In any case, you'll need to complete them all for the "Hercules" trophy/achievement, so I hope this helps somebody.
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