The first thing you should do is get your Bloodsail Buccaneers faction to honored. To do this, you have to kill a lot of Booty Bay Bruisers. But doing this tanks your 4 goblin factions (Everlook, Ratchet, Booty Bay and Gadgetzan). That's why you do this first. Once your Bloodsail rep is at Honored, you can go to Dire Maul: North and do Free Knot over and over and over.
Free Knot is a quest inside of Dire Maul that requires you to loot a Gordok Shackle Key, which you then turn in for reputation and receive a chest of leatherworking and tailoring goods. You can get the key from any random mob in North, but specifically 4 NPCs have a higher chance to drop it than normal: Guard Mol'dar, who is down the ramp right in front of you when you zone in; Guard Fengus, who is found near his chest in the next big room; Guard Slip'kik, who is right near Knot down in the inner part of Dire Maul North; and the Gordok Bushwhacker, who spawns after you loot the Ogre Tannin, on the platform above Knot.
At 375 reputation per turn in, it takes about 243 turn ins, as a non-human, to get Exalted with the four goblin factions. So learn to love this place! You'll be here a lot. Unfortunately, you're not guaranteed a key every run. A helpful way to slightly speed this up is to turn in the Ogre Tannin in Dire Maul. To get this you need the following:
Bolt of Runecloth x4
Rugged Leather x8
Rune Thread x2
Ogre Tannin x1
You get the Tannin from the basket above Knot and you turn the items in to Knot, so turn this in as many times as you have materials to before releasing him with your key.
So you're Honored with Bloodsail and Exalted with The Steamwheedle Cartel? Well, you're only about halfway done. The Insane requires your Shen'dralar reputation to be exalted as well. Shen'Dralar faction is only raisable through turning in 3 Librams in Dire Maul to the appropriate NPCs -- Libram of Focus, Libram of Protection, and Libram of Rapidity. From Neutral to Exalted, you need to turn in 86 of these in any combination.
I would suggest turning in as many Librams of Focus as you can as they are the easiest to make of the 3.
Libram of Focus
Pristine Black Diamond
Large Brilliant Shard (4)
Skin of Shadow (2)
You can farm all of the materials for this one in Scholomance. That's how the pros do it. (86 times.)
If you're still going on this because you really want to be Legolulz or Xxarthasxx The Insane, though, you're still not done. Not by a long shot.
Ravenholdt would be my suggestion next. This faction is actually fairly easy to level in comparison to the others, but it's almost definitely the most boring.
First thing to do is to go to Hillsbrad Foothills and wander over to Durnholde Keep. Syndicate NPCs give 5 Ravenholdt faction per kill. You can go from neutral to 11999/12000 honored just through kills. That means you're killing 4200 of these little fellas if you're 0/3000 neutral. After you've maxed out honored the only way to get faction with Ravenholdt is to turn in 5 Heavy Junkboxes at 75 reputation per turn in. Either level a rogue or make friends with one or be prepared to spend a lot of gold to get the 1470 that you need to get through revered and in to exalted. But if you're truly Insane, the thought of leveling a rogue to get your main a title doesn't faze you all that much. The junkboxes come from any level 50ish mob and require 250 pick pocketing to start getting. It will make you weep at how painfully boring it is to farm, but you want to be THE INSANE. Keep going.
Okay, so. You've farmed the goblins, freed the hell out of Knot, and you've developed carpal tunnel from turning in junk boxes and librams. You aren't done though.
The last step in Insane in the Membrane is to level your Darkmoon Faire faction to exalted. In 3.0 with Inscription this is a lot easier than it has ever been. The Rogues Deck that you can make with Inscription rewards 25 reputation per turn in and you can do it multiple times and in any location. You summon a turn in NPC with the deck and she stays up for about 2 minutes before despawning. You can turn in as many decks to that same NPC as you possibly can in that time. At 25 reputation per turn in, it'll take you 1680 turn ins to go from neutral to exalted. That's a lot of low level herbs used to make cards.
So you've done it. You've earned the title The Insane! You will be envied by people working on the achievement, asked how you got it by people who are unaware of the achievement, and scorned by people who know about it but aren't willing to do it. But it was all worth it. You have an awesome title!
According to Blizzard, being Insane means you have a lot of gold, a lot of patience and a lot of time. By the time you complete this achievement you won't even need a title to remind yourself how crazy you are. You'll have doctors in white coats willing to do it for you.