As far as I understand it you declare it’s coming from Bear when you place your card face down. The normal attacks are the cards that every one has access to. So Bear can use Dive, Assault, Focus, Sweep, Spike, Cross, Grasp, and Block. So if Miska is the one Striking and she declares it’s coming from Bear it telegraphs more of what she can do.
I mean it’s just one way to go about getting cards in the discard. When playing against Miska I found myself burning a lot of cards to move in order to avoid Bear and get close to her.
Against Lily I’d say Chain Strike is super crucial. If she declares a strike she can only beat it by playing The Magic Bullet Ult (and then even that only works at range 4). If Kaden declares the strike she has no way to stop being pulled into range 1 with you and now you have advantage. There are still counters to this such as Lily playing Focus (so she can’t be moved) or Sweep (to trade super well, but you still have advantage).
Havoc Call is another great attack to use when you’re just trying to get it. Allows you to completely avoid damage at the range Lily wants to be fighting at.
Once you get in on Lily you’ll probably want to have Focus in hand. She’s got a couple of fast attacks that move you way back. Focus will stuff these hard. Even if you can’t play it EX you can still get a ton of good value out of it. Then use your retrieve cards from discard effect in order to pull Focus back into hand so the threat is always there. Focus should be a big part of you mix up vs Lily. Focucs will wreck Double Tap and Excessive Force. However, it loses to Hair Trigger (if you’re at range 2) and Mug Shot. Luckily Kaden has his own moves that can beat those (EX Rising Host beats both).
Against these long range fighters EX Rising Host is super strong. It will trade poorly with some attacks but it will beat all of Lily’s special moves as long as she’s at range 1-3.
You’re probably right that Fusion Bane and Double Charge Executioner aren’t very good against Lily. I’d probably avoid using those. However, the Chain Extension Boost is extremely relevant vs Her and allows you to beat her at her own game for a turn. Secret Weapon Boost is also a good one and can be used to get that crucial card you need (Like Focus).
So in any given mu different cards are going to be more and less important. Against Lily Cross is good for its Run Boost and Focus is amazing for its attack. For me, especially when I was super new, I had a tendency to want all the Special attacks to be the go to attacks and for the normals to be lesser used. Sometimes the normals are the stars in certain mu. Also I wouldn’t be too concerned about playing EX Focus (especially if you aren’t in EXCEED mode) it has too much value as a card to use both of them up in a single attack (unless of course you can get them right back with Silence or Dark Tide Summons).
Still seems like a trickier mu because Lily still has a lot of mobility but maybe some of the above could help.
It seems like Kaden should have an easier time vs Eva. She’s a build up character too but a slower one. All of Eva’s Specials and Ultimates are subpar (she needs to get Boosts into play to make them worth anything). She also doesn’t hit hard so your Guard should allow you to trade well vs her. What about Eva where you struggling against?