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Kael is a bad choice for Fireknight, and even worse at stage 13, due to his affinity. He has a 4-hitting A3, but this has a cooldown of 4 turns (booked) and his other skills are not usefull here.

Alure is not an ideal choice for stage 13 as well. FK 13 is force, Alure will have weak hits wich can't crit and therefore don't reduce the turnmeter. In addition she will receive strong hits, and her base def of 793 makes her very squishy.

I think Armiger can help you. Good affinity for stage 13 (and 20!) at FK, he can survive some hits in the waves (15195 base hp, 947 base def at lvl 60) and you can use him in some other places as well (Spider, Scarab King).

Alure is always a good choice. With 100% CR and a decent amount of speed, she'll keep FK from acting, since she'll generally act twice before FK can act once, which should be enough time for the rest of your team to strip his shielding. She should be able to control his TM fully at that point.

I use her on my FK 20 team, which has the same affinity as FK 13, and have no problem at all.

Alure is fine for FK13, as well as 20, she does her job despite the weak affinity, but indeed only if there is a reviver on the team or the team is just so strong that they blast through the waves without taking much damage. In this case he has a Gorgo, so it could work. 

As for Kael being bad for FK - yes, but he does need somebody to do damage on the waves... although, maybe if he doesn't mind taking a long time on the waves, he doesn't need an actual nuker there. 

@Swiftage Stag Knight is excellent on FK - two hit A1 with decrease speed debuff helps a lot! If your SK and Fellhound can both do some damage on the waves, maybe try SK, Coldheart, Alure, Gorgorab and Fellhound. 

Many thanks for the input all. As a follow up: how important are masteries, ascension level & getting to 60?

Critical. All three are 100% critical. Masteries crucially unlock Warmaster / Giantslayer for your CB teams, which is an absolute necessity if you plan on using leech to keep your teams alive. Ascension level 3 unlocks or upgrades an ability, while 4, 5, and 6 unlock accessory slots, all of which are very important. And level 60 allows you access to the aforementioned Warmaster / Giantslayer.

Have the same problem, stage 13 keeps failing.

Alure, keal, apothecary, Moutain King, Zelotha

:Edit:It just worked anyway