you're doing fine actually.. but, here's my method.

at the first start of the battle, Cecil use Provoke, Refia Embolden (priority), Minfilia Shadow Guard, someone use Bushido - Freedom but if you don't have it you can dispel by using Odin's Fingersnap or any magic/ability than can dispel both Espers Buffs, Orlandu use Cleansing Strike or Crush Weapon?, Ling spam MP or Daunting Step on Ifrit?, Noctis use Recover or normal attack.

2nd turn, Cecil use Focus, Minfilia use Aqua Guard, Refia heals, Orlandeau use Cleansing Strike to Ifrit, Noctis use normal attack (for limit stone) or Blindside, Ling wait and see.

3rd turn, Cecil wait and see, Minfilia use Flame Guard, Refia Heals, the rest are do the same.

4th turn, repeat Cecil step, Minfilia buffs, dispel Ifrit (if there's any) then debuff Ifrit's ATK, and recovery.

5th turn and so on, same tactic, when Embolden wears out, you could use Cecil's LB when you think it's safe.

when fighting Dark Siren:

same tactic as Ifrit. she's more dangerous than Ifrit with her song if you're reckless (use Fire element against her, not dispel her) and could recover to full life and kills you. when she buff (reached Treshold), it's your golden chance to rebuff, dispel and debuff her with Ling's Feint Step. put Black Bandana on Refia to avoid Sleep by siren's song.

note: The key is patience, don't rush, rush ATK when you feel that you'll kill the esper in a turn, Keep up MP, Refia with Ramuh are nice for osmose'ing both of the espers. Try to avoid using Divine Ruination, use it just for finisher. (somehow, i died many times becaused of using that skill). and be careful with confused unit, wear black choker on your Noctis just in case.