I am going to restate Grailer's advice in a much nicer way. Because unfortunately his way of saying this in such an arrogant and mean way won't actually let people read what he is actually saying even though it is very much a good strategy.
Swift for first pull, switch to Foe after you make it to killing area, immediately do a Rain of Death (this will help with keeping the tank alive if they are not super overgeared and allow the WHM to holy more), IF your WHM is bellow 2k MP and the PLD is below 800ish (just my numbers I use with my group I do it with you can adjust for yourselves) through up Ballad after the pull. If Ballad is not needed then swift song so you can keep up with the (more thank likely) sprinting Tank/WHM/BLM (BRDs can't sprint as much cause of needing the TP to help kill). Single Target down the tonberry. Personally I don't put up Foe here because it dies so fast anyway.
First Boss (after mobs are locked out) through up a Soul Voiced Foe and unload on the boss. The next pull is a pretty long run. There is no need to have ballad up for this pull as the PLD should be full from the boss fight by using Riot Blades and the WHM will have plenty of recovery time while running. So I through up swift Song. Once mobs are gathers repeat like the first group kill.
After last mob dies switch to Swift Song. (Again no need for Ballad here as there is plenty of recovery time). Once mobs are gathered repeat the AoE kill by switching to Foes and unloading (making sure to have Rain of Death up to help the tank of course)
Pudding Boss is the same as the Gobbu. Wait till mobs are locked out to cast Foes (I don't use SV here because I want it for the final boss and we go so fast the timer isn't up if I use it here). Unload and AoE the adds and stuff (I usually only see one group of adds we kill and then we ignore the last one because they usually pop right before it dies).
The next pull is actually pretty short and you may need ballad if your WHM is below the recommended amount (mine being 2k). Again the PLD is probably full or should be from the boss fight.
Rinse and repeat a Group AoE kill pattern with Foe up and a RoD at the start and watch them melt as you BLM LBs them.
Final Boss: right at the start fire circle and then SV Foe. Then get on your Single Target kill rotation. If your group is good (geared) enough the WHM shouldn't need ballad so you can just keep Foe up the whole fight. I usually run out of MP right when the bugger dies.
Grats you just did the best a BRD can do when it comes to things that are not related to your gear. ^^