What you need is two controllers (or a friend) and some shiny loot, more specifically 15 Legendary items, 20 purple items and 45 blue items. If you have $3 millions, that will help too.

This is what you do:
Start a game with the second profile, the one you do not intend to boost, or have your friend start a game. Drop all the before mentioned loot on the ground. Dashboard if you want. You might have to join several times to get enough loot, but that is what you need in order for this to be effective. (You can skip the blue items, and still get a decent amount of Tokens, so that is a matter of choice/opportunity.)

Join this game with the profile you want to boost, and make sure you join with a brand new character. Pick up all the loot to complete the Loot Challenges. Drop it on the ground again. Trade minimum $3million with your friend/second controller, make sure to trade it back.

When all this is done, you will have gained 166 rank per Challenge completed (1+5+10+50+100).
If you managed to get 4 done, it equals to 664 Rank.

Additional Challenges you can choose to do, if you have the recources:
- Buy all Eridium Upgrades from Crazy Earl. (Requires an Eridium Drop Save)
This takes your total Rank gained to 830, + a few extra points here and there for i.e trading with your friend.

Names of Challenges:
Nothing Rhymes With Orange, Purple Reign, I Like My Treasure Rare, For The Hoard, Waddaya Buyin'?

Leave the game, make sure you have no items and no money before you do so, and join again with a brand new character. Rinse and repeat for as long as you can be bothered. ;)