Looks like I'm needed here. Let's try not talking even though it is going to be a right-before-sleep post.
Against parasoul, your air normals aren't as good as parasoul's, so you don't want to j.hk or j.mp brainlessly.
J.mp can be good to stuff her out, but you'll need the proper spacing.
Try getting way above her using glide or super jump+double jump, this will give you an approach angle she can't really counter on her own (napalm pillar isn't really reliable when against an opponent falling fast, it will most likely hit you after you landed so you'll be able to guard...plus you were in the air since quite some time so she didn't have any reason to charge down). But that makes you vulnerable to an assist call, so be ready to bait instead, AIR pushblock if possible (you don't want to eat overheads), elbow drop after that (nobody ever expects it)...
Every other air approach will be likely to be countered by j.lp j.hp, so your aerial game will suck against her most of the time.
Learn how to deflect her tears consistently, the projectile AND the trap it leaves (learn the timing for the explosion, it's a projectile too so you can deflect it), don't let her get any advantage in the ranged game. After some trap explosion deflects, parasoul may start to use detonate to trick you. That's fine, she doesn't get much advantage from that, but you may try to bait it armoring through with tumble run, that way you may get a free 360. Remember that it recovers super fast, so if you're faar away, just do that to get closer and run stop, don't commit too hard.
Beside that, I use A LOT bella's armor tools into super cancels. Against jump-ins, mashed napalm pillars, pressure, resets, hp lnl cancel 360 or dynamo is fanstastic!
With proper spacing and timing, mgr can be great to counter jump-ins too, as she can't really change her air path, but it's kinda hard to do and sucks hard if you failed.
Napalm pillar xx bikes means free 360 if she's not too close to the corner, else try to pushblock the bikes to punish.
Bait the lvl 3 to counter it with yours (you can counter it on reaction postflash so go for it), DAF will armor through it and hit her after the end of her invinc. If she cancels with call, she will probably won't react nor guard it (too much shit on the screen to see).
If you were in the middle of a normal when she does it you can deflect and guard immediately after.
Brain shutting down, can't think anymore.