So the team that you use rn has a big flaw: no CC. That 1 role can make huge differences with the waves, so if you don't use Bellower for anything else, try to farm stun set for him. 

And yes, you also have too many dps champs in the team. Kyoku great protection, Bad-el can posion and also that double continous heal should suffice in terms of healing, Kael is I assume is the main posioner, which is good, you just need another protection champ, maybe a shielder, or just 2 CC champs with stun or freeze. If you can only use freeze gear, do it, it's I would say will be 80% as effective as stuns. The only difference is that you deal only 75% damage to frozen enemies, but it's better to damage an enemy that can't hit back for 75%, than to deal 100% but die from their hits. 

I also struggle with CC in my Dragon 20 team, because MM sometimes just doesn't put up his stuns. So I would say, even if it takes 3-4 mins to make a run, consider bringing in more CC, keep Kyoku, Bad-el and Kael, and see what happens. In dragon the difficult thing is going through the waves. Once you reach the dragon with a whole team, that's no problem. Especially with Kael+Bad-el.

This is only a suggestion, maybe there is someone more experienced, who will give you better advice. Still, think about these

I agree with Wandor, your problem is the lack of control debuffs in your team. You have Crimson Helm, she has some capability for control with her A2. As a provoker, you can put her either in a frost set (chance to freeze the attacker if you get hit, great synergy with provoke) or counterattack set.

Another option would be Achak. He should freeze most enemies in the Dragon dungeon, I guess. I never tested it, and his mechanic is a bit odd (freezes enemies with higher atk than def, burns enemies with higher def than attack).

Honestly - based on the gear you have shown, I think you should just go with solo BEK. You need to get a bit better stats, but not much moreso.

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This is BeK's gear. Previous Screenshot was Kyoku's. I pulled BeK just last saturday. He has masteries but no books. I imagine Regeneration gear must be also a good option for soloing, right? If so, I should start farming FK because the only set I had is on Kyoku now ...

He's quite low on ACC tbh. I see that he doesn't have banner on yet, but even with banner, that's +96 ACC at most, you might want a bit higher for stage 20 dungeon stuff. Like around 220-ish, just to be sure. Maybe that's your plan, I don't know, I'm not nitpicking, it's just something I noticed, thought it might help

I mean, I use Toxic on my BEK for soloing. His self heals are more than enough to keep him alive. You just need him to be faster. You want 208 speed minimum. And yes, you need masteries - you want the two speed-boosting ones (in red and blue trees)

Yes, you're right, but that's the gear I have. I'd be quite glad to have a banner and "only" 200-ish.

I do have Masteries on him.

One added problem is lack of a proper <DEF, Bellower's is the cheap one and not very effective.

Last iteration I was using HK with a Shield set instead of Genzin. Not good results either.

As long as Kael gets to the Dragon with Kyoku and and BeK I'm fine (in level 17), the problem is that sometimes it's not the case.

Well, I guess it's ... patience, I'm missing champions with certain skills and gear on the champions I already have ...