This was a fun one. All 50 challenges in the game (including the 13 "main" challenges) must be completed under the par times. These are represented by a gold star (a silver star means you completed it, but not under par time.).
Most challenges CANNOT be done on your first run, since you only have a handful of units to use at the start. You unlock more units as you beat more challenges. Whatever tactics work for you to get the times are up to you. For example, I love playing as the Allies and building Harbinger Planes and Mirage Tanks, but that may not work for everyone.
A common (albeit cheap) tactic is to play as the Rising Sun and spam out Tankbusters from several barracks', and spam out Chopper VX's from War Factories if you have enough time. I only did this on a few levels, but again it's a personal preference.
If you are having trouble with a few levels, I recommend checking out the videos on this Youtube channel:http://www.youtube.com/user/razattack1337
(These videos are from the PC version, so you probably won't be able to move as fast, but you'll get the gist of it.)
Also, if you have a request for a specific mission walkthrough, please let me know which one and i'll see what I can do.
Lastly, if you use the "Red Alert Button" you'll automatically finish that level with a time of 99:59. You gotta do it legit!