The Insane difficulty is unlocked after completing the game once already, on any other difficulty.
Insane offers a nice jump in difficulty. Prepare to die a lot, since you will be getting damaged at a faster rate than before.
You can do this on co-op, and your co-op partner can be on any difficulty they would like. However, they will not be getting the achievement if they are on a different difficulty.
I did this with a friend and both of us were playing on Insane. There are a few sections in the game you will probably have some trouble with.
Act I: Right before you get to Landown and right after the Corpser pops up from the ground, you will have a Brumak firing missles at you. Stay on the turret and keep blasting him with bullets.
Act I: The split-up between the Hotel and the Rooftops can be problematic. I have been killed during a cutscene for this, but the main problem is Tai. Tai is a bit of an asshole and tends not to revive whoever is playing as Dom. After this whole part, be sure to hang onto your Mortars after defeating the Brumak. This will help you during the graveyard fight.
Act II: I don't recall there being any seriously bad spots in Act II, but you do get introduced to snipers for the first time here. Snipers will damage you just enough so that you're completely vulnerable. If shot by a sniper, be sure no one else is shooting anything at you since you will be downed. I'm not sure if you start encountering foes sporting Boltok pistols yet, but those guns hurt like a bitch if you keep getting shot with them.
Act III: Carrying the bomb can be a little bit of trouble. Be sure to have either the Snub pistol or the Gorgon. Shoot the Wretches that are far away and stick to meleeing when they are close.
Act III: The razorhail will hurt like crazy. Make sure you actually get inside of the train cars right away. If you accidentally jump out to the side, you're done for.
Act III: The whole Centuar sequence sucks. The vehicle controls like crap and you'll take a lot of damage. Troikas will easily kill you within 2 seconds, so make sure the gunner kills off everyone before pressing onwards. Always stop to heal.
Also, taking down the Tower requires the driver to do some fancy driving. The gunner should take care of all of the ground troops and the two Troikas right by the tower. The driver should then start driving down the hill in reverse. When Marcus yells, "Dom, hit the tower!" the driver needs to boost right back up the mountain since you'll be getting shot at like crazy.
Heal, creep your way closer to the building and have your gunner blast that tower to all hell.
Act III: Troika will kill you in about 2 shots, so watch it. When you get on the Locust gunboat, get into cover and stay in cover. Don't even bother shooting at any of the other ships trying to attack you. I noticed that when my co-op partner and I got into cover and never peaked our heads out (or blindfired), the enemies just stood still. Save your ammo and keep switching sides of the ship depending on what side the boats come in to attack you.
Act III: The Leviathan boss is pretty much the same as always.
Act IV: When you close up the dam, have one person go down into the water to activate the enemies and have the other player stay by the switch. The person who stays back should probably have the longshot rifle handy so they can easily kill off the guy trying to get the water to flow again.
Act IV: Right before finding Maria, you'll have to kill a bunch of enemies in four waves. Wave 1 is from straight ahead and consists of 2 Bloodmounts and wretches. The Bloodmounts are the worst threat, so keep shooting at their heads (the Gorgon pistol works well here) and melee the wretches. Wave 2 is the same, except from the other direction with worse cover. Again, kill the Bloodmounts first.
Wave 3 has two grinders, so kill those first before they get in too close. Then get rid of the drone varients. Wave 4 has a few Theron guards mixed in with various drones. Dispose of the Theron first.
Act IV: When setting off the beacon, you'll have a few Reavers come in to attack you. There is an awning of sorts that will protect you from some of the Reavers' attacks.
Act IV: When on the rail cars, be sure to focus your firepower on those incoming Reavers. If a single one of them hits your car, you'll have to start over again. I recommend sticking with the Lancer for this part.
Act IV: When you have to split up in the large hallway leading to the throne room, it's a good idea to pick up the Mauler's shield. It'll protect you for a little bit. Towards the end of this hallway, you'll have to shoot at your partner's side (Ahead of you, but on their side). Get rid of those guys with the Torque Bows, since they will kill you in one shot.
Act IV: When you fall into the trap, immediately grab the wheel and start going back up. The other player should try protecting the guy turning the wheel. You can avoid this fight entirely by doing this.
Act IV: The only things you have to watch out for when fighting Skorge are the Ink grenades and the Tickers. Everything else is pretty simple: dodge the pilliars and chainsaw duel.
Act IV: The reaver sequence isn't too bad. You don't seem to take as much damage as you did in the Centaur.
Act V: The entire act is easy, especially after getting the Hammer of Dawn. You might run into a bit of trouble with the split up right before the Hammer of Dawn, but it is all about pacing. Everything's pretty smooth during Act V, though.
If you're doing the Casual-Insane method, you really don't have much to worry about. The Casual player will be doing most of the work (killing), while the Insane guy will be chilling in cover and avoiding the fights.