One of my favourite challenges is to take on Skelly Galleons solo. I recommend doing it at the end of a session if you have a load of supplies left over, it can be very good practice. I know it's annoying when it happens out of the blue, but I would take it as an opportunity to practice. If you do sink them, they can give you really good loot.
They can be very tough but there are a few tactics you can use. As WolfManbush says, try to avoid their broadside. If they get all cannons trained on you and manage to kill you, it's pretty much game over. If they are firing any emote curse balls (jig, weary) they are even more tricky.
One tactic I use is to lock the wheel in a quarter turn circling them and raise the sails by a third. For whatever reason, this can confuse the AI (works better on Skelly Sloops but it can help with Skelly Galleons also). If you get it right, they will probably start spinning trying to focus your ship.
Use firebombs on them, as long as they're not shadow skellies on board at night - if they are, fire a flare as well. This helps clear the deck and give you some breathing space. Firebombs on mid deck will also help clear out skellies running to repair. Cursed cannonballs are also your friend, if you have barrel, ballast, weary, venom and/or jig balls, they are really useful, I find.
There is also the old tactic of rubbing up against their side and staying there whilst bailing water onto them (skellies can't bail water out). You'll be too close and low down for them to shoot their cannons at you, but be aware they will be trying to shoot you with guns.
I recommend keeping an eye on your health as well, it can be easy to lose track on that when you're overwhelmed and the sniper skellies can be a pain. Stay calm, focus and time manage. After a bit, you get a sense for when you do and don't need to go below deck to patch. One hole is not a major issue but try to keep in your head a mental image of what is happening around you. It's all about prioritising what needs doing and when.
It's not easy, but it can be a lot of fun and there are very few genuine PvE challenges in the game nowadays.