I'm not an Aang supporter but I suppose it won't hurt to have a try. I'll assume Providence is in his first key (since idk which key is being used).
Getting the Avatar State out of the way, Aang will use it when he feels threatened, as seen when Ozai was getting the upper hand in their fight (though it's mostly because he could tap into it again after being hit in a specific manner). He can protect himself before using the Avatar State by encasing himself in earth, which is what he did in book 2, but could tap into it quickly enough to avoid being damaged any further (should he be hurt in any way). In a matchup such as this, he'll probably be in the Avatar State faster than you can expect.
While Avatar State is a big wincon for Aang, he's no slouch in his normal form. Looking at the location, there doesn't seem to be any water at all, so his water bending will be limited (he could be creative and use his sweat, but it'll still be limited.) If it's in the ship itself and not the location where the ship has crashed, Aang can only depend on air and fire. Otherwise, his earth bending will come in handy by a lot. (I haven't played Risk Of Rain so hehe)
Regardless of location, Aang will be incredibly agile and acrobatic, using air bending to his advantage as he either closes or maintains distance (via his air scooter or glider among other things). I'm not sure what projectiles Providence uses for the danmaku, but he should be able to shield them from him via his air-bending (he managed to do that with Ozai's firebending, even managing to protect himself from his comet-enhanced flames). His air-bending is the best bending he has. Aang's fire bending should also not be underestimated, as he's able to go toe-to-toe with Ozai in that department. (That's how much I can say about it cuz Aang only uses fire well into the final episodes and I don't have much to work with. Hope the actual Aang supporters can have a say about it).
If the battle is in the confines of the ship, he's still as agile as I've explained above, but he wouldn't have much to work with unless he goes into the Avatar State. Providence will have a better chance of winning, but Aang will be pushed to use the Avatar State faster that way.
If it's on the crash site planet thingy, Aang has earth-bending to work with. Probably lots of earth. Firstly, his earth-bending could resist Ozai's hot-ass comet-enhanced flames, holding out on several fire blasts till it crumbles, at which his air-bending will help shield himself. Offensively, lots of boulders and rock shenanigans will ensue, including bounding his arms and legs. Aang will also have lots of room to manoeuvre now that it's in an open area. High agility, acrobatics, air and earth, along with the occasional fire.
I don't have an answer for the teleportation. Does Providence use it often and frequently? If so, he'll just have a harder time landing hits, but he'll do fine.
Even if Aang doesn't get to use the Avatar State and lose this matchup, he won't be going down that easily.
Edit: Wait worms as in Gilded Wurms? Well, that will heavily depend on the location, as I've said. Earthbending will help immensely as well as his agility and acrobatics. Air Bending will also go a long way. Then again, seeing two giant worms trying to attack him would probably make Aang shit his pants and immediately enter the Avatar State.
