In what has been a bit of a theme recently, we have a game that is a solid game with an oversexualised veneer. “ADVENTURES of CAPTAIN Becky” is actually a pretty decent platformer, but with a plethora of options for you to modify your character, and unlockable suits that fit into a variety of fantasy stereotypes. This is a bit more platformer than Dead or Alive Xtreme is volleyball, but only just.
That said, there’s doubtlessly a market for each of the two things this game is trying for (the 13 year old heterosexual boy, and the person who actually just wants to play a good platformer), and there’s likely even a market for something that does both. The extensive character customisation options would even be progressive, if they didn’t seem so tightly aimed at fantasy fulfillment. But I suppose, is that much different than the depiction of men in Muscle March and/or Cho Iniki? Or the depiction of women in Bayonetta for that matter?
So the bottom line: there’s a decent platformer here, and you’ll either find the presentation appealing or it’ll be something you’ll have to look past. I doubt very much you’ll have absolutely no reaction to it, though. 80 Microsoft Points with a large number of levels and, for better or worse, lots of customisation options.
Here’s what the developer (sakura) has to say about the game:
“The adventures of pirate captain Becky! Clear all stages and defeat the enemies! Play a total of 24 stages in EASY, NORMAL and HARD mode! Unlock the Extra stage! Collect 5 different costumes!”
Writings of Mass Deduction 
Wow. This looks great! I don’t think it’s quite for me though. It looks to be as much of a puzzler as a platformer. Whoever is playing in the YouTube video certainly has it memorized, but from watching it, I’d guess that a lot of trial and error is involved.
One note of feedback to whoever made the video. From your play, I would have guessed that the coins are rather pointless. I question why the author would add them to the game and show a video where they are essentially ignored. Don’t let this detract from the overall though. I’m very impressed!
The game is a puzzle platformer, but the puzzles are very mild. I finished the game (on the default difficulty setting, at least) in about 20 minutes. The puzzles are more about making sure you dodge the obstacles than anything more taxing.
I really don’t understand why the tackiness is present in this game. It was one of my earliest XBLIG purchases, and I originally played the trial simply because I like pirate-themed things (I know, not the best reason!) To my surprise it turned out to be fun. I really think the developers risk turning off potential buyers, but then I suppose they attract others to balance it out…