N-air straight up, DI back if she's dashing at you. You land right on her head. You can also do this with D-air, you just need to anticipate earlier.
The Gentleman is great for defense if she's not expecting it.
If you expect her to jump at you, a quick U-air toward her intercepts a lot of things she can do.
At very low percentages you can chain her a couple of times with JC'ed D-Throw (I know it doesn't seem like it, but you can if you're quick). At slightly higher, she'll probably try to DI and tech away, which you can predict and turn into a knee or more combos.
I do a lot of jab-jab-grab setups. She can grab you between the second and third jabs, which is why you should throw in your own.
For edge guarding, edgehog to force her onto the stage, then knee her off the ledge or roll on and F-smash.
Do everything you can not to get off the stage. Double-sticking helps. I fight two Shieks who edgeguard me with D-smash, preventing sweetspotting. It's possible to still grab the edge if you know falcon's ledge-grab range REALLY well. You've gotta be in the "it-didn't-look-like-I-could-grab-the-ledge" range.
All that being said, a good Shiek's strategy will usually be to needle you and force an airborn approach where her u-air, b-air, and f-air are ridiculously overprioritized (along with f-tilt and u-tilt). If you space it right, an N-air where you land way in front of her can be an okay approach if you catch her mid-needle, or even better, a d-air where you land behind her.
You've gotta keep the pressure on her or she's going to needle the crap out of you. Space your dash-dancing so she can't f-tilt you but you're close enough that she can't needle.
Hm, I think that's all the tips I've got. I play good Shieks more than any other character by far and I come out on top about 65%. That's not to say somebody else won't have better advice...