This may be a surprise for some, with GameFAQS even listing it as a fighter(somewhat rightly so, as it comes with Guilty Gear X2), but the Judgment side of this package is a side scrolling hack 'n slash.
PSP (2006, published by Majesco in North America, Europe, and Australia)
1-2 players(most likely via wi-fi)
(Sol-Badguy with an alternate color scheme, my guess would be having chosen him with the Circle button)
Controls:
Square - weak attack
Triangle - medium attack
Circle - strong attack
X - Jump
X & any action button - jump attacks
Forward & any action button - stronger attacks(Circle will throw when extremely close)
Down & any action button - low/crouching attacks
Double tap Left/Right - run
X & double tap Left/Right - air dash
run & any action button - running attacks
R - reverse attack
L - Burst(first fill the Tension meter underneath the health bar, then fill the Burst meter. It's kind of like a desperation move in any other beat 'em up, but it instantly depletes the Tension meter, instead of costing health, and it's not necessarily dependable for doing a lot of damage)
For any special moves, there's an option to view them in the game's pause menu. The yellow moves, which would be supers in a fighting game, require at least half the Tension meter to be filled before pulling them off. When the burst meter is filled(it drains if you don't use the burst move) you can use the supers until it's gone(usually 3 times if you're quick enough).
There are no continues in the traditional sense, instead the game recognizes the section of stage you left off and allows you to pick up the next time you start the game, and choose the character you were playing as. There are extra lives(all items in the game are walked over), and one thing you can do if you feel you need more to fight a boss, is to go back to stage selection, and choose one you know where the extra life is, and continually build lives by getting it, and heading back to stage selection.
Some stages have a bit of platforming(use the run/air dash if you're not comfortable with their regular jump), and others may have vehicles(well, a mechanical lizard anyway) to ride(jump on them), in which the action buttons do something different. If you fall in, it's not instantly fatal, but you do lose a decent chunk of health. and some areas have multiple gaps.
Bosses can be tricky, early on they're stationary and spamming attacks to try to keep your character away, but it's never too difficult to get in there and give them a few good shots. The trick is to figure out how to avoid their most devastating attacks.
In the beginning you only have 5 characters: Sol-Badguy, Ky-Kiske, May, Millia Rage, and I-No.
You unlock characters as the one you're playing as meets them. This guide explains who unlocks whom, as well as some of the stages, bosses, and a few hints at the end:
https://www.gamefaqs.com/psp/928252-guilty-gear-judgment/faqs/51405
This one explains in full detail how to unlock Judgment:
https://www.gamefaqs.com/psp/928252-guilty-gear-judgment/faqs/44834
If you don't feel like looking at it, the basic gist is to explore the hell out of stage 6-1 until you've found the 7 letters that make up his name(if you're not sure when you've picked one up, you'll see 3 yellow ?'s).