Updated list, thanks for the comments.
So, here are the places you need to do for this to work. I am going to assume you already have the regular versions done (I forget if you have to do that before you get Time Attack, but anyway).
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They don't take nearly as long as the normal modes of the levels. There is one that gets very very large, but most of these are done in about four minutes. I got all the Time Attacks done in about an hour or so.
Let me know if I missed any, it's possible that this popped and I had already done one sometime earlier.