I'm a comparatively new player; the first GHB I was able to actually win ANY difficulty was... I forget if the re-run of Narcian or Michalis was first. I think Narcian. Regardless. My point is, I'm not at the point where I'm willing to tackle Infernal yet.
But I'm proud of myself: I was able to, after much trial and error, take down Lunatic difficulty.
3* Level 35 Olivia (base kit, no inheritance)
4* Cordelia, again with Base kit as high as 4* can get. +atk -def
5* Cherche, one of my first pulls as a 3*. I've put work into her: Brave Axe+, Bonfire, Deathblow, Drag Back, and her base Fortify Defense (which ALMOST screwed me over, but not quite) +spd -res I don't care if her boon isn't optimal. She's gotten me out of SO much shit.
5* Leon with base kit, +HP -spd. Very lucky pull; literally my first colorless pull from his focus banner.
I had Cherche (and the team) eat the Savage Blow hit from the Firesweep on the first turn so that I could smack him with Cherche and back her out on my next turn, leaving Cordelia to murder the red mage. Leon started the second turn next to Olivia (and out of Panic Ploy) to oneshot the axe flier. The next turn or two, he spent letting the archer shoot at him while everyone else stayed out of range; here's where Cherche's Fortify Defense almost screwed me; Leon was sitting in Panic Ploy, and the first attack by the enemy archer benefited from a reversed Fortify Defense; Leon survived the second (no stat alterations this turn) with 1 HP. Meanwhile, Cordelia sat around while Cherche Brave Axe'd the sword-flier reinforcement in the face, killing it thanks to a Bonfire proc. With Leon at 1 HP, it's time to act. First, he takes out the Firesweep Lance flier that's moved in to his south, then Olivia lets him finish off the archer (the order of these two doesn't really matter), then Cherche nukes the axe flier that moved in from the top right corner. At some point during or after this, Cordelia nukes the Sword Cav reinforcement from the bottom left after running out of his attack range so as to not get hit first. After that, it's Cherche's show; she flies north, just out of the new Red Mage Cav's range, while Cordelia and Leon just get the hell out of dodge. Once the red mage and the green axe cav move up, Cherche attacks the red cav from the side, and Drag Back places her just within range for a dance from Olivia to let her finish off the Axe Cav.
I felt so good about it. First time I've beaten a Lunatic GHB without looking at other guides and suggestions. Loooots of trial and error, and it took quite a while to think of using an archer. Longer than I care to admit >_>;