I'm planning on getting the Torgue DLC in 2 weeks, when I go home for spring break. It looks awesome, my Axton is all about Torgue, and I can't wait to start farming Pete!
Anyway, as someone who doesn't mind farming in chunks up to ~3 hours, I can tell you what I do to make it less dull and stuff.
First of all, there are a few legendaries that aren't worth farming at all. Thunderball Fists from Captain Flynt, Hammer Buster from McNally, Fastball from Boll, Unkempt Harold from Savage Lee, and Infinity from Doc Mercy are all impossible to find during PT 2.5. Don't try to farm these bosses! I wasted a few hours myself before finding out that they literally DO NOT drop them. Someone found a script to improve drop rates for uniques (legendaries) for each specific boss. Apparently, this script caused every boss to drop their legendary 100% of them time, except the before listed bosses still never dropped them. This, along with the fact that there is still no conclusive video evidence of the drops, is enough proof for me to stop farming them.
Something I try to do when farming is fill out badass challenges. Some tedious challenges can get knocked out pretty quickly by doing them over and over during farming runs, and then you can eventually prestige. I just prestiged for the first time a few days ago.
To be less bored, I generally find a nice long Youtube lecture on astronomy, origins, music, or whatever other interesting topic. This takes my mind off farming and lets me learn (maybe?) about cool stuff simultaneously.
Also, there is definitely an order to farm in, boss-wise. I'd say go Hunter Hellquist -> Knuckle Dragger -> Bunker -> anything else.
Hunter Hellquist is a must, just because his radio station is so close to where you start in the Arid Badlands Nexus. It might take a while to get a Bee shield, especially since drop rates are decreased in True Vault Jumper Mode, but perservere and you won't be disappointed.
Once you get your Bee shield, head over to Claptrap's place. You should be able to kill Knuckle Dragger from up on a cliff, looking down at him. When he dies, his loot will scatter all over his little plateau and you can use a sniper rifle to see if an orange pistol dropped. This pistol is the Hornet, and will make Bunker a piece of cake.
Head over to Thousand Cuts, go up to the Bunker and start killing him with your Bee + Hornet until he drops a Sham shield. The Sham is a shield with a ridiculous bullet absorb rate (mine is 87%, max is 94%) which will keep you nearly invincible while heading to other bosses' locations to farm them.
Hope this helped, if anyone else has any questions just ask.
Edit: Also don't hate on the Flakker. It's hard to figure out but jesus it is a monster