The other solution didn't work for me. I went to the Lair and couldn't get to the raid boss. After doing some research this is how I got to kill the dragons.
First I completed the campaign. I then went to Mr. Torgue in the starter town to pick up the quest "Raiders of the Last Boss". He will only give this to you if you completed "Fake Geek Guy" from him already.
Pick up the quest:
https://www.trueachievements.com/gamescreenshot.aspx?gsid=32...Now head to the Lair of Infinite Agony (if you completed the campaign you know where this is) and head to this location on the map:
https://www.trueachievements.com/gamescreenshot.aspx?gsid=32...Donate some Eridium to this guy, the wall behind him will vanish and you can go for the dragon.
https://www.trueachievements.com/gamescreenshot.aspx?gsid=32...I'll make the solution look a bit more pretty later! I wanted to get it out there quickly. :)