Dance Central

To quote NathAttack: "Hopefully this maintains its ABSURDLY high TA-Ratio forever ;D
Even though I know it won't, not actually difficult at all. Still, man can dream, right?"

Well, he's right! Each Jazz Square is basically the same move. The clue is in the name, you make a square with your feet...I have no idea why it is called "Jazz", I don't imagine doing that move to Jamie Cullum.

Enough digression! Each jazz square has the same basic steps. From your starting position, cross your right foot over your left, then bring your left foot behind your right foot, then bring your right foot in line with your left, then left foot back in its starting place. If your having trouble, practice away from the game. On each step the arms are doing something different, but that depends on which of the moves you are doing.

In "Hey Mami"
Jazz Square slow is basically the Jazz Square at half speed and comes right at the start of the song (on Hard at least). Arms are slightly up and bent, the arm needs to be pushed out slightly on every beat.
"Hella Good"
The Jazz Square here is the fifth move in (on Hard), exact same thing with feet. But your arms are curling (like a bicep curl) on every beat.
"Push It"
The Jazz Square is after # Working up a sweat! # . Exact same as Hella Good's but goes in the other direction. That's left leg over right first. For Jazz Square and I do only the first two steps before jumping into the 'I'.
"Brickhouse"
The Jazz Square is near the beginning of the song on easy. A normal jazz square but make "hook" arms.

This video is not the game, simply an instructional video on how to do a Jazz Square. If you still cant get it after breaking it down or through the song, practice by yourself using that video.

Warning: that instructor is telling you to do an extra step which you don't need to do in game!

Songs that have Jazz Squares in them:
Hey Mami (not on easy)
Hella Good (not on easy)
Push It (not on easy or medium)
Brickhouse

Due to the order I traced this down in, I dont' know if you have to pass all squares on all difficulties and in Break-it-Down of if you just have to pass all the jazz squares on each song in any mode on a difficulty where they show up. I suggest using Break-it-Down on these songs to nail the squares on hard to see if it unlocks and if it doesn't, then at least you've got pratice for Perform-it.

This achievement works the same way as all of the moves related achievements, it can be done in Break It Down mode, where you have to get only one(!) green check on Jazz Square moves, the rest of the song's moves can be failed.
The songs with Jazz Square are:
Hey Mami (medium or hard)
Hella Good (medium or hard)
Push It (hard)
Brickhouse (easy or harder)

I did this all in perform it mode and you don't have to do it on every difficulty and in break it down as well
The easyest way to do it is with -
Hey Mami - on medium
Hella Good - on medium
Push It - on hard
Brickhouse - on easy
Jazz Step and I does count (thanks to Witchiro for the correction)