This may sound bad, but is actually rather easy. Put the game on normal (you won't need any skulls, but bandanna may be good if you're bad at grenade jumping.) I did this on both Cairo Station and Outskirts.
If you do happen to die, just save and quit and resume game before it re spawns you. If one person dies in coop it voids it for both of you so be careful.
Outskirts was far easier for me. Take the root over to the REX SWORD and then descend to the ground where the snippets would normally shoot at you and continue down the alleyways until you group up with the marines at the Hotel Zanzibar.
Once there simply follow the marines to the phantom. Kill the covies that deploy and get in the warthog. Drive it straight to the end of the level ignoring everything. And boom! Achievement. You should also get the par time for this as wel as the blind skull and Rex sword if you've seen a video for them.