She's a tough villain, but there are a few ways to make teh fight an easier one.
I do subscribe to the idea that any villain can be beaten with any combination of heroes, though some definitely make it harder than others. that being said, here are some of the general tips, strategies, and thought processes that I use when fighting her.
Prioritize Her Support Structure
This goes beyond the sip, in some ways, though getting rid of it will certainly make life easier. By herself, she's not that bad. She has a single nasty hit (on her starting side), but her strength lies in her crew.
The main ones to get rid of ASAP are Mable and the Battle-forged. Both enable her to get extra card plays, which will make your life hell. the others will hurt you, but they will strip you of resources, go after the weakest, and enable La Capitan to grow stronger.
The ship is a good thing to get rid of, but if don't prioritize it over everything else. The reason is because La Capitan has a card that can get the ship back from the trash- so if you pour everything you've got into getting rid of it (potentially ignoring crew, ongoings, or setup), theres a chance that her next card will bring it right back at full health. Look for ways to accomplish multiple objectives or ensure some breathing room- like scouting her next few cards to see if its safe to get rid of the ship, or locking her deck, or getting the ship out of the trash. In the long term, if you can get rid of it ASAP, go for it- but be aware that unless you know otherwise it will be back, and at the worst moment.
Its Dangerous to Go Alone (Take This)
Team synergy and tactics are an absolute necessity when fighting her. Always be on the lookout for ways to help other heroes. You're going to be losing ongoings/equipment, so make sure that you have some sacrificial stuff ready (or at least be aware that you may lose what you have).
Any card/power that gives you some breathing room is essential. If you've got a specialist (like Ra or Chrono for damage or the AA for support), it helps to do everything you can to make sure that they can do their thing before getting your own cards down. This is because generalists can adapt ot changing situations (usually) better than the more specialized heroes, but the specialists can usually crank out wondrous things once they are set up. Spend a few turns protecting them, helping them do stuff, or sacrificing your ongoings/equips for them. They'll pay it back in spades once they start setting the world on fire, blasting crew members full of holes, or (in the case of the Argent Adept) letting everyone else go crazy.
If you've got a team of generalists, stay flexible. Try not to obsess over the "perfect build" (something I am still learning how to do), and make the most out of the options you have. There will be frustrating moments...but you also may find new combinations and tactics that you never considered before. An example I learned recently (for Unity) involve using her "Scrap metal" card to take a low-hp bot back into my hand AFTER it does damage. It keeps them from being munched by the Battle-Forged.
On the topic of Hero Order, it definitely matters. Heroes that support others through an external focus (by increasing their damage, letting them draw cards, play cards, etc) tend to do better at the start of the turn order. Heroes that deal high damage tend to do best at the end, where they can perform clean-up duties. In the example of fighting La Capitan, it helps to have the heavy hitters go later in the order because it gives the other team members time to scout out her deck (to see if any dead ships or crew will pop right back out), get rid of her ongoings (since she has one that makes it painful to take out her people), or generally weaken the minions and bring them into killl range.