Basically, I found that being grounded is a really good idea, try to get them into the air before you go aerial. Make sure that he never gets right above you: that's just terrifying. Dtilits and ftilts are going to be your bread and butter, use them to control space.
A way to tell who's in control is by checking your spacing. If an upsmash can hit him, he's too close or right above you. And if a utilt can hit him, shield asap.
Try not to be in shield all the time, mixup dash dancing so that you bait a grab. If he grabs you should get a very easy punish. Another way I like to bait is by moon walking into spot dodge, but don't constantly repeat this.
If he plays a strong egg game, you want to play in the midrange of campy and aggressive, meaning each time he eggs, scoot closer and razor leaf. You need to get him from not constantly throwing an egg. If you get close enough you can dtilt him and follow up.
When it comes to edgeguarding, don't put all of your eggs in one basket. Use 1 rar jump to get out there, but don't ever use your DJ, you will just waste it. If you can hit him before he jumps, that's great. If not, go back to ledge, and begin this flowchart:
- If he's far enough out that you can get back onto stage and either RL or seedbomb, do that
- If he's close enough, refresh invincibility and wait for him to get close, if he hasn't used his DJ yet, do a neutral getup and wait to dsmash.
Getting a dsmash on a Yoshi is probably the best way to kill him, as he has to jump to get back to the stage and might get hit again.
Yoshi is boring to fight against, just be wary of his grab and you should do alright.