This includes the challenges. You can check your progress on a song by selecting it and looking at the rating next to the Perform It! option. The letter will indicate the highest difficulty, and the number of stars will indicate the rating you got. For example, if you've 5 starred a song on hard it will show H*****.
Your score dictates your star rating. Your score is higher if you can keep a good multiplier going. It counts up 1 every time you have a Flawless or Nice on a sequence. 1x is lowest, and 4x is highest. If you move a body part wrong, the wrong part will glow red on the character. For example if your feet are correct and your arms are wrong, the characters arms will glow, but his/her feet wont.
Also, make sure you keep moving during the Freestyle section. If not, you will lose your combo. You can tell if you moved enough if it says Flawless at the end of the freestyle section (instead of Nice or other). All you have to do is make sure you move the entire time to get a Flawless. Just wave your hands at the screen if you need to conserve energy.
Lastly, if you're still having a hard time, watching Youtube videos can help. Riffraff67 has a lot of songs on his channel being performed on Hard. He does a picture-in-picture, so you can see how he moves in relation to what the dance move is. Mightymecreative is also a popular Dance Central video poster.