Just from your first match I might suggest forgoing doing plunge after 133 and just do 133~purple pain AMP. It puts you at the exact distance the lightning comes out and you can do close or far depending on if you read a forward or back roll. If you do plunge you're left with pitiful amounts of hit advantage so trying to do purple pain off there is going to be a waste of meter if they know the MU. Also remember to punish stuff like flying kick with F2 1+3 KB. I'll try to put more stuff in later but yeah that's what I got from the first match.
EDIT: After watching more:
- remember that you can machine gun lightning (though none of them really blocked it/tried to do something and you unfortunately got hit)
- poke~AMP katar is a powerful tool since not a lot of moves can interrupt and you're completely safe and if you get the katar they are eating 9% (katar is so good lol)
- remember your JK OS into geyser kick for more damage
- probably good to practice those wave dashes so you can maximise your damage from those full screen lightnings
That's all I've got. I bloody suck at Rain so grain of salt I guess. One extra thing I'm personally trying to do more is his sweep, since it's got very good range, gives Rain a low profile and is decently fast, but since Rain isn't really walking, I don't really get to use it a whole lot since dash D3 is easier to use than dash sweep so
shrug I guess