See picrel for hardmode shard distribution

Notable shards:
>Hard 6-4 XXL Beernox
>Hard 6-3 XL Guala
>Hard 4-4 XL Akaoni
>Hard 3-4 XL Dallawan
>Hard 2-4 XXL Kahfka
>Hard 1-4 XL Shibahiko

If you can beat 6-34, you can beat every single hardmode stage with no problem. Except maybe Beernox, since the big slimes are bulky.

For 6-34 use Code:B and a strong healer (I had Beernox 35, Meng 30, Code:B 30, Baade 35, Tayangsuyi 35 in that order). At minimum, defend on turns 8 and 16, the boss will use their special around that time. Other strong attacks are on turns 5 9 13 and 17. The boss has a passive that gives him a permanent attack boost for knocking out members of your party.

The thug's weakness is his jaw. Once you drop him down to 1 HP, it should trigger the minigame and then he'll delete himself.

Also, you need to eliminate the slimes first no matter what, they give the boss a damage reduction boost that makes him impossible to beat otherwise. Happy farming anon