Sheik vs jigglypuff
Ok I feel like throwing in my two cents.
Remember your sheik and you have great aerials and needles. When afar you can force jigs apporch with needles or just walking up to her while respecting her b air and f air hitboxes alike. Generaly jigs will either straight up out beat you in the air or you will trade. This how ever doesnt stop sheik from taking the match what so ever. As kirby kaze said
Sheik's Bair > Puff's Bair if you do it coming under her. The trick to competing with her aerials is to not be on the same horizontal plane. Be slightly under her, ideally. If she doesn't want to get under you, get on a platform and toss sewing equipment from the air.
I have also had success with falling down off platforms or the air with high droped back airs and got clean hits. Your back air works great but i would advise you to mix it up with n air as well or d tilt. Your back air aint that amazing vs jigs lol.
Down tilt as teczero has stated also works very well for finishers in stead of f tilt. It also sets you up for a nice up air which is sheiks
BEST finsher on her. Im not quite sure at the % it kills plus it varies by what stage your on. It works wonders regardless.
Down smash works good on jigs while she is on the ground. Kira mentioned something about mango being able to rest you if jigs sheilds it. I havent seen it yet. Regardless it catches jigs off guard and is great damage.
I dont like forward tilt much at all. I use it randomly to throw jigs off.
Up tilt works if they are dumb enough to be directly above you or to poke them threw platforms while remaining safe.
Retreating f air or neutruals work if you she is on a really high % and dont mind a chance of trading with her. Remember her aerials dont kill but yours does. Her aerials lead into gimps and edge guarding. Thats how sheik is typicaly gonna die. Unless they catch you in the lag of your up b which leads into forward smash or a rest.
If you do manage to grab the ledge be smart about getting back on stage. Ledge hoping back on stage then throwing neeedles is great. But
DO NOT attempt to rush her down after that connects. Get out of there asap. You do not wanna be near the legdge vs jigs. Waveland into sheild works as well. Sometimes get up attack of the ledge.
Jigs gets pressured out when she is conered. Space those back airs. You want the trade at high %.
If she whiffs rest down throw slap or u air(if at kill %) run. Sheik has no gurantee hits after that. Play smart play cool. Dont be recklessly hitting her because you will lose.
percents 0-80 I say its about building damage as you see fit. Aerials needles and if your lucky off of grabs. Which reminds me
DONT ****ING GRAB UNLESS YOUR POSITIVE YOUR GONNA LAND IT!!! jigs can crouch under it and rest you. Dash attack is also very unsafe. Use these moves wisely if at all.
After 80% its time to wrap it up.
As far as stages go play gay. RC allows to escape the pressure of her back air for a large amount of time while beaing able to aggrivate her with needles and aerials as well as a really low celling. Kongo jungle 64 allows you to recover in multiple ways and play the hit and run game very well. (PockyD mentions this)
Here are some vids and stuff
Nicaboy sheik vs hungrybox puff
http://www.youtube.com/watch?v=l37mIuLVIqw&feature=related
http://www.youtube.com/watch?v=clPZ2qIg4Fk&feature=related
Drephen is really good vs puff
Drephen shiek vs Sliq puff
http://www.youtube.com/watch?v=lVFnSesuD5I&NR=1
Read da sig kiddes altough its probably not true lmao. Anyway hope i helped.