Robin isn't exactly a popular character in the competitive scene, probably because his/her sluggishness is unattractive to high-energy, mountain dew chugging competitive players. You can use common ignorance to your advantage.
Winning in 1v1 as Robin is mostly based on how well you react and read your opponents, also about how quickly you can make them panic and behave erratically. If you're against fast opponents, you're going to have some trouble if you don't read them real soon as they WILL use their speed against you the moment they know this unknown character moves so slow. I suggest making good usage of grabs and dash attacks against characters like Sonic. If this fast character "prefers the air" try baiting air dodges with short hops then follow up with the appropriate smash attack or more preferably Nosferatu to avoid the usually unexpected Perfect Shield
I'm more of a FFA player, so I often play 4 player FFA on FG. Performing well as Robin on this can be quite stressful against two skilled players as characters you do not have much experience against and possess tools that are very anti-Robin(projectile spammers such as Link and Pit for example), worse so if the fourth random is cannon fodder that regularly gets decimated by the better opponents whom also have time to counter attack/defend your offensive. Robin, imo, is a great character for controlling FFAs if your opponents ignore you, and I'm not talking about Thoron spamming. I'm mostly referring to matches where at least one opponent gets annoyed by your projectiles and stars gunning for you and flops over on his face in the process(totally not a Tripping joke).
But, what if this opponent you irritated, is actually skilled? This is where your opponent reading helps. If you know the character you're facing then you would make him look stupid with your both ways D-Smash, Arcfire/Arcthunder zoning, and exploiting vulnerabilities as best as possible.
Another tip: Unless the opponent is completely watching every move you make, always go for the tomes/sword you drop then wait for your opponent to read you wrong(such as another Neutral B charging)and let 'er rip! Be unexpected.