When I was DRG, I specifically swapped to Sylvie to maximize my attack bonus. I rarely had to worry about dying since mobs died so fast.
1 Sulvie (UC) - Wil use frailty+ entrust fury, which is helpful. She's also a remarkable curer, and, if it weren't for the fact that she only has cure4, she'd be my #1 trust of choice. Will erase/-na as soon as it pops, so she's definitely a keeper.
2 Cherukiki (will run out of MP after about 5-8 fights)
3 KoH
4 [Use Qultada for first pull, get Chaos/Corsairs (or fighters), then dismiss. He'll interrupt your SCs too often.]
4/5 Varies: Joachim/Ulmia, Shantotto II or August (or AAEV)
The last slot kind of is up to you. Do you want additional haste? If so, Joachim/Ulmia will be cap you out, but not 100% of the time. This is a pro/con you should consider. Are you multi-stepping (like you should on DRG)? Then use Shantotto II and Go for your Trishula 4step or non aeonic SC. She'll return the most addition to your DPS. If you're not concerned about her dealing damage, you can drop her for a tank trust, which will help out Cherukiki a little bit with not having to re-summon her so often.
DRG is pretty flexible when soloing Apex, so you can take your pick from above. Between jump timers, spirit link, and MA from qultada's resummoning, you may be able to handle the loss of the crappy songs Joachim/Ulmia puts out. I hate relying on both of them for marches, since they almost always will never keep them on fulltime. Personally, I chose to do Bats in Dho + Raptors in Moh, specifically the latter does not have attack down and has pretty low def/hp.
DRG typically needs less healing, so I opted to not use Yoran/Apururu for DRG. Sylvie's buffs are job-specific, though, so I can't recommend her for every job (like NIN). But she's good in my book.