To start: I used to add a header to these reviews, but since it often made the review too long to submit, I've opted to leave it on my Backloggery.
Gameplay: oh boy another puzzle platformer brought from XBLA time to not recommend it- Wait what? It's actually not half bad? ...you sure? Huh, so it is. Adventures of Shuggy is a puzzle platformer whose main attraction is many stage gimmicks. One stage may have you rotating the entire stage, another one may have you teleporting all over the place, another may have you be zombified so that you can jump and only jump... there's a lot of gimmicks. There's a lot of stages as well; 112 stages in the main game and 40 extra in the teleporter-focused mode. Out of all these levels, there were only seven or eight that I felt were legitimately kinda terrible. Fortunately, there's a lot more than that for levels that are really quite clever with, y'know, actual puzzles.
The platforming itself isn't bad, and in fact there's really only one complaint I have about the platforming, and that is inertia. Shuggy actually has a lot of inertia, meaning that you can very easily end up falling off of a ledge due to your own inertia. You can kinda deal with it after a while, but it's still kinda obnoxious even once you get used to it. Another thing that could be a problem for some is that Shuggy is actually pretty dang fast. There is a bit of precise platforming here and there that could prove tricky for some due to how fast and how inertia-laden Shuggy is, but it never was the top speed that gave me any problems.
There's also boss battles in the game, although they're more akin to boss battles from a game like Donkey Kong '94. I did quite like all of the bosses, and they all took at least some thought and careful planning to defeat. Again, they're, y'know, actual puzzles. It's hard really to talk too much more about this game's gameplay, as the core mechanics are quite simple, and the complexity of the game comes from these gimmicks. There was one gimmick that I enjoyed only about half of the implementations of (Shuggy temporal cloning) and one gimmick that I didn't like at all (wall-crawling Lemming carting around). Apart from those two gimmicks - and they're largely toward the beginning, so if that's causing you duress, just push through; it gets better - I had a great deal of fun with this game. Some other reviewers mentioned a lot of waiting around, but honestly; it's not all that bad. Unless you have super-ADHD, it's really not going to ruin your day. Unlike a lot of puzzle platformers, I can see myself coming back to this game in the future. For $5, it's a great deal. For the $0.49 I picked it up for during the Winter 2013 sale... that's highway robbery. 8/10.
Story: There's not much, really. It's all told through a faux-comic book style presentation. It's honestly not worth rating, as it for the most part stays on the backburner for the gameplay to shine through.
Graphics: It takes a bit of a hit here for two reasons. Reason one is that this game either windows in 720p or fullscreens in 720p. The portiness of this game is quite obvious here, since the 360's maximum resolution for gameplay was 720p. As for the art style... it's alright, but it really does have that "XBLA-look" to it. I'm not the best at pinning this sort of thing down, but I think it has to do with how the XNA kit handles gradients and sprites in general. It's not bad, but once again, it shows that this was once an XBLA game. Kinda disappointing, honestly. 2/5.
Sound: Sound design isn't the biggest deal for this game; it's mainly some obvious sound effects and that's about it. As for the OST, it's not a thing that I'd get to listen to on my own time, but it's good enough in the context of the game. It's a decidedly jazzy OST which is partly why I'm not too keen on it, but that's because I'm 2dumb2jazz or something. If you're into that kind of thing, maybe you'll want the OST for yourself. 3/5.
Overall scores are: 8/0/2/3; 6.5/10. A game with great gameplay design that is unfortunately hindered by some less-than-amazing AV stuffs. Again though, for $5 (and especially for $0.49), this game is a great deal, and will provide you with a day or two of mostly good times.