My friend which I practice the most mains him, and just like
Crome
said, this is not a fun match up, unless you really feel like shooting lasers all the time.
Bombs are the main problem here, since R.O.B is so big, getting caught by a bomb is easier than it seems, and if you do you might eat some follow ups. It's the same problem with his boomerang, if it hits, you may take a bomb next and so on.
Up tilt strings are annoying, and if you are in the air you need to plan well how you are going to land, because his uair hurts a lot, also do not try to air dodge it, it lasts forever.
Tink is so tiny, sometimes grabbing him is a pain, getting near is not a good idea anyways.
The only way I can play this is using the the good ol' gyro + laser spam, gyro set up at the ledge if they are going for a tether recovery, a very well timed dair if they go for uspecial. Pressuring off stage with fair does also work.
I have had some luck approaching with Arm Rotor, but I don't really recommend this.