Does anyone know ways to become Overpowered in this game in Hard Mode?
The earlygame is going to be a struggle no matter what you do.
Start by going for Yterre first, simply because she can be recruited without a fight by stealing the crystal shard from the chest in her bedroom and sticking it in her mirror in the gallery.
With four members, you should have just enough power to defeat Jyla and recruit her if you get a little lucky in the fight. With five members, you might be able to take down the Gunslinger and recruit her too.
If you have the DLC, you can recruit Wind without combat if you know exactly what you're doing, though getting back
out of that building requires either fighting a boss or suffering a Bad End.
By now you should have enough cash (or be easily able to get it; the Crooked Traders in Valua are filthy rich) to afford Nuan's asking fee. And this is where the fun begins.
Train Nuan so she learns Shirogiri and Aogiri. Stick her in a Soldier Shell (also requires DLC) and use Upgrade Kits on it. She now can trade HP for shield points without taking up turns, then Shirogiri to heal the HP back, or Aogiri to mow down groups. The biggest threat is now the possibility that the enemy might have Blow Away to launch her out of the active party.
You could also try something very silly with Annie in a Soldier Shell using Showdown, though I haven't tried that one yet.
EDIT:
I decided to try out the new Arachne class. It's so close to greatness...
Unlike Soldier Shells, an Arachne can wear headgear. This means she can wear a Noble's Mask and have Faceless Maids copying her Combat moves... or she could, if not for the little detail where she can only "broadcast" her first move each turn to the maids to copy, and subsequent moves will be ignored. This means the maids will only ever copy one Predation (from initial CP via Passion) and on subsequent turns Prey Juice or Torment. Annie as an Arachne cannot use Spell Bullets (Arachnes cannot equip weapons, including Spell Pistols), and Showdown simply does nothing. Sadface.