This will most likely take some time and get your fairly frustrated. You must finish Trial mode on Normal with all characters so must have them all unlocked in order to get the achievement. I highly recommend going here http://www.youtube.com/profile?user=kalelulen4&view=vide...
and watching the video for whatever character you're trying to pass the trail on. Watch and learn the spacing he uses and also how fast/how many hits a move takes to know if you just aren't doing the moves fast enough or if you need to cancel certain ones, etc.
But keep at it and don't give up. If you get really frustrated just skip that character or go play some ranked battles or arcade and try to tackle it later and maybe your fingers will be more cooperative :P
And I did all of them using the 360 controller, so it is possible and you won't need a stick, but if you're serious about SF you should probably look into it.
If you have any questions about a certain move/combo don't be afraid to ask, I'll try to help you out as best I can.