While the other solution is excellent if you don't have a co-op partner, Insane difficulty is made a complete breeze if you can play in co-op. Unfortunately, you cannot use the supergun in online co-op, but entering "Revenant" in the code screen will still unlock Insane difficulty off the bat, just as it would for single player.
That said, the biggest tip for co-op is to always have one player be the scout and rush groups of enemies and the other be the sniper and kill enemies from a distance. This is useful for two major reasons.
1) The scout can intentionally engage enemies and get downed with that cluster of enemies around him to make the sniper's job easier. Enemies do not disengage and/or look for new targets just because someone goes down. This makes enemies easier to snipe, or if you're lazy, to drop a trip mine on top of.
2) If the scout goes down, the sniper can use spirit vision to resurrect him from any distance. And because the sniper is sitting at a suitably far distance, he doesn't need to worry about being attacked while doing so. The caveat to this is that unless most of the enemies in a section are dead, there's little point in resurrecting because the scout will likely just get downed again almost instantly.
If you don't have a co-op partner, but you do have two controllers, the sniper can become your safety net. Just use him to resurrect yourself anytime you're downed, and you should have little problems progressing. The sniper will also be automatically teleported along occasionally when the scout advances, so little work needs to be done to continually reposition your safety net.
Update: Playing in split-screen co-op also has the added bonus of still allowing the primary profile to use the supergun while also having the safety net of a second player. Enter the code "BlowOffSomeSteam" at the code screen and you then have access to a one shot, one kill weapon.