If this thread is part of some kind of elaborate joke about how old SS2 is, then disregard this post.
Ukyo is a little weird to get used to if you've mostly played simpler characters like Haohmaru or the ninjas, but SS2 Ukyo isn't that hard.
The only 2 special moves you need are his swallow slash and after image. You can use the snowfall slash qcb + AB if you want (only use the AB version, the others are too slow) for block damage, but you don't even need it.
Learn to pull swallow swipes off the ground (db, d, df, f, uf + AB). You need this skill in both games, but it's stupidly easy to do in SS2. When you do the move "off the ground," it's an instant overhead (have to block high, hits crouchers). Learn to do it from a forward dash and also after a low C or two. His standing kicks (the slides) aren't really worth using for this setup, or ever, because they can be punished severely.
Ukyo has/had a dirty high/low corner game, his jump AB is an OK starter, his jump CD (which hits multiple times) is a better way to force guys to block high, then one or two low C's (or none, to mix things up) to force a low block, then a swallow swipe off the ground. Mix this up with throws against human players to give them fits.
If you want to be annoying, learn how to throw swallow slashes on a back dash. Tap b,b, then db, d, df + AB. Do this right and Ukyo will throw a swallow "under" the screen and have it pop up on the other side, just like a regular projectile.
Ukyo's A and B slashes are fast in SS2, but they have spotty hit detection. His low B -> qcf + C is one of his best combos, but he has a different low B up close (the overhead arc slash which is useless and gets you killed). Either learn the range on his far low B or don't use the low B. His low A works just fine to do low A -> qcf + C as a pressure move.
Ukyo's standard "punish a big mistake" combo is close standing AB -> qcf + CD.
Never use his POW special, except for very early air defense if you see them coming a mile away. It's a worthless move, but he doesn't need it. So overpowered in SS2.