This is the strategy I used.
Either 4 player XBL or what I did personally was 4 accounts/4 controllers. Shared gold is a wonderful thing.
*If you are using 4 controllers, sign into all four accounts BEFORE loading the game because you will have a problem getting into a game.
You are going to be either doing the 2nd or 3rd dungeons, I did the 3rd one personally. I wouldn't use the first one because the boss fight is too hard trying to throw the guy on the platform.
Next, choose the class of weapon you want to use, I personally used the Gutrender, just make sure the other 3 are using any other sword to get the "Someone has to change" achievement.
You are going to want to reset the levels until you get the Glass Cannon and Lifesteal boosters in the beginning of the dungeon. It is critical you have both. This allows you to pretty much solo the entire dungeon. The resets are worth the time it will take to finish it. All you pretty much have to do is hit RT.
So once you have those, the 3 people *NOT* getting the achievement will be running off the edge and dying. Do *NOT* revive them. When all 3 others are dead you will be able to run through the depth, only killing the enemies you need to progress.
Only go for chests that are on the way. The rising platforms for them take forever to come up in Co-Op so just run past those, you will have way more gold than you will need.
The gold is shared, so all the gold you pick up, a percentage goes to the other players, you are going to want to buy the power up that increases your health by 100 on the person going for the achievement, nobody else buys a power up.
Now all you should buy is lives and re ups for your special attack. At depth 4, everyone revives and then spends all their gold on lives. They then die again and you run through the level.
You should have way more lives than you should need at this point.
I'm not going to go too in depth on the boss fights, because there are already guides for them, you should have a good understanding of the boss fight mechanics for the boss you choose to beat to get this achievement.
After this the person running through the dungeon should get this and the achievement for everyone using the same class of weapon.
Any questions just comment and I'll try to help you out.