Found this invincibility glitch. I can't take credit for it, just sharing it here. Sorry if this has been posted already.
You must have at least 3 people, one person has to be a siren with the Res skill. Have the other two people down themselves with like a rocket or any other means. Have the siren hold X to start reviving the first person who wants to be invincible. While holding X, use your action skill on the second person while still holding X to revive the first person. After both players are revived the siren can release X.
Now the first person that was revived by holding X is now invincible and will auto second-wind every time downed. Also the siren will earn 100xp every time the character second-winds. The invincibility lasts until the person that is invincible or the host saves and quits.
Now have fun beating those annoying DLC bosses!
Edited to add: Tested it and it works with 4 people as well so 2 people can be invincible. Also this is for the Xbox version. Have not tried it on PS3.