First you have to take out the pauldrons and the ailettes, which inflict magic damage. Each one has a different element attached to it and each has its own weakness. The magic they cast will become stronger over time. After those are defeated, you can then effectively use ravagers and saboteurs against him. He is susceptible to slow and curse. If you have a synergist in your party I would also suggest you cast haste, and renew it often. His stagger point is 250%, but he may often begin to cast destrudo. If you are very low on health, you can choose to heal, but if your health is reasonable, then use the relentless assault paradigm. The more you attack him while he is casting this spell you will notice that he will grunt, and this means that destrudo has weakened in power. If you dont attack him at all, the effects can be devastating, always leaving you with the barest of health. He has no weaknesses so the only way to inflict mass damage on him would be to get him to stagger
You can also inflict high damage on him by using Vanille to cast deprotect, deshell and imperil on him. This allows Hope to bolster your attacks with enthunder or enwater, further increasing damage. Most importantly, make sure lightning's health is above 1400 to survive Barthandelus' Destrudo attack. This 2nd strategy is generally more useful to under-levelled parties, where Vanille's debuffs and Hope's protective magic become particularly useful. Lighning can also be the party's strongest COM at this stage, before Fang's Strength has a chance to sky-rocket.