Basilisks: Generally try to claw you. One of their "red eye" moves is a forward sweeping fire breath, another one, they jump into the air and land for AoE. They can also jump backwards, but this isn't redeyed. They can also do a 180 degree spin, which hurts you if you stand to close. This is preceded by a "hip swing" sort of warning. If you stand too far, they can also shoot a laser at you (can't remember if redeyed.)
(I think they also have a zig zag jump, can't remember if it's them or the Nagas.)
I don't remember if the projectile is red-eyed or not. But it does give a red circle on the ground for where it is going to hit. And I think it is the Nagas with the zig-zag jump.
Kumas: Again, generally try to punch you in the face. Redeyes include jumping (warned via squatting), and ice breath (raises head.) They can also trample you, if you're not careful (when they run.)
Personally, these guys are good for learning, since they are slow.
Not sure if you just never had it happened or you didn't remember to state it. They can get enraged and start to glow (with lightning effects), when this happens they move much faster and can be quite deadly. So, when they start to glow, switch to a defensive/dodging fighting style.
Nagas: Biggest assholes of the bunch. Generally do slashing attacks. If it raises it's forward legs, it's likely going to do a groudpound, so give it some room. They can do zig zag jumps in rapid succession, straight jumps, and sideways jumps (these wrecked me the first time.) Can shoot fireballs (right hand will sheath weapon.) Red eye indicates it will do a forward stab the ground attack (several times.) Indicated by it's sheathing of both weapons.
There's a few other characteristics for each I probably left out, simply because I hardly see them use it. There are probably the most common attacks they use.
I haven't fought these in a while so no comments.
Though what I stated for the Kumas actually can happen for other BAMs as well, they get "enraged", start glowing and get faster movements and attack speeds.
Edit: I forgot to say that BAMs stay enraged for a set time period, so you can just let them "cool off".
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Spoiler for Hiden:
i was only kidding about the rug. 
besides that is animal cruelty. 
*has my avatar lick you*