Fire knight 20 is force affinity. Alure is mvp use her a1 to prevent boss from regaining his shield. She is magic affinity and may weak hit though level 21 is spirit affinity and better for alure. Visix can escort alure through the waves with her provoke then you have to break his shield with multihitters and alure will drop his turn meter. Fire knight hard is similar except more hits needed to break shield and freeze debuff drops his turn meter ally attack champs shine here.

You want to nuke through the waves quickly. Embrys, Quintus and monkey may be good chocies for that, whoever hits hardest

You'll defintiely want Alure and coldheart for FK 20 normal. Alure should only use her a1 on him. coldheart should open with a1 to get the shield down

Rhazin and fayne should also be considered to place def down and weak on the boss. Off the top of my head I don;t see another champ who has both. though you could use deacon and cuddles the puppy (forget his actual name) and they both have aoes that could be used on waves

First team i would try, without knowing your stats and gearing, would be alure, coldheart, quintus, embrys and rhazin

@MooredRat, I made the team you described in the last line of your post, and they finished in 109 turns. I see the point in this team; I can quickly break shields, but they're too weak. Only Coldheart dealt significant damage twice. I equipped them with lifesteal and regeneration, SPD above 200, CRate 100, and ACC from 200-300. And the difference is 40 turns too much. I can equip them in the optimizer without sets, but then who's going to heal them? Your team doesn't have a shield or healer, so I probably won't even get through waves. Any ideas on how to upgrade this team? 

Of course, I set up multi-hit attacks on round 3, disabled AOE, but aside from A1, I left the skills for one enemy. Team power 308 K.

Edit: still experimenting, exchanging champs, no result.

Sorry, that'll be a matter of gearing and stats.

Try visix in a lifesteal set? she'll bring some protection, but might not improve your turn count though

Ideally, you wanna get weaken and def down on FK as soon as you bring down his shield. And you should have enough tm redux so that he never gets his shield back up

For Normal, you could try a CA Team with Valk, Visix, Rhazin, Stag Knight & Coldheart

For Hard, you need freezers, ideally A1 Freezers. The only ones I see are Criodan & Yakarl, so they need to be on the team.  You can certainly make a CA Team work in Hard with A1 Freezers.  Same with an Ally Attack Team.  As you climb higher in Hard FK, multiple Ally Attackers with A1 Freezers are the best way to go.