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1. Don't jump as much. Sheik bodies people on the ground and is very fluid on the ground. Jumping in as your initial approach is probably wrong 99% of the time. People want to SH Fair or Nair a lot, I say nay.
2. Get used to her grab mixups. Dthrow is solid, but you have Bthrow as a mixup in PM that wasn't there in Melee. Less GG Melee Dthrow, but more potential for hard reads and trickiness. Also, pick up boost grabbing as it's useful to catch certain characters if they DI away from Dthrow. In general her boost grab is really damn good, that just happens to be the most prominent example I could think of for using it.
3. Brawl stuff tends to get transferred over to PM. Brawl's Pivot grab, RAR, DACUS, Glide Toss (wasn't specific to Brawl IIRC, but is 1000x more prominent there), backward edge snapping for more recoveries, etc. Oh yeah, she can crawl in PM due to Brawl. It's kind of good/lame lol
4. You need to be aware of what options might backfire on you. At low %'s, it can be hard to tilt or smack people due to Crouch Cancel. If you can probably land a grab instead of a tilt early on, chances are you should go for it. There are exceptions, like if the opponent is in the air or did not CC, but overall smarter opponents tend to not give her that luxury very often. The cool thing about Sheik is that you usually don't have to force things on the opponent. She's pretty mobile on the ground and decently versatile, you can tend to wait and react based on what your opponent is doing. Like when you play Sheik, the gameplan doesn't have to be "Ok I need to get close and tilt/grab him". You can sit back and charge needles or try to deal with the other person's approach, or don't commit to an option while getting closer. She's pretty good at not "having" to do stuff in neutral.
There you go. Onwards to the glory of playing Sheik!