Mana definitely has issues. She fights markedly different than the others.
To start with, begin your stages by disabling lockon, and zooming out.
Mana's combos home in and/or spread shot so naturally she doesn't need lock-on as much.
Tapping Triangle is an ideal way to fight up close. Hold it down and it will progress through multiple effects... power shot -> machine gun shot-> homing shot. You can move a little while charging.
Use Hold O to blow away opponents. With Lock-on disabled, you can phantom dash to evade attackers.
When locked on, Mana's attack animations obscure the enemy but she is able to use Launch from relatively any distance using her Circle Projector. If the arena is already cramped, then just stay locked and make effective use of this.
Mana's basic attacks don't cause flinching until she's on a very high drive with lots of Heat - but the moment she reaches that level of power it is all over, the enemy is never getting close again. She generates plenty of synchro and can abuse her specials to punish enemies that get locked into attack comboes when she's already dashed or evaded away.
Indeed her chief advantage is 5-star punish skills, she has no need to approach the foe. The moment they whiff, she can unload on them.
The key is knowing what to do in a panic situation, when the enemy is on you. Use Triangle taps to fight back, jump and do a ground pound, or hold Circle to blow away. Resist the urge to Launch, which is so effective for Ranka and others... Mana's launcher is far too laggy and if you use it up close you'll probably get hit.