ROB NEEDS (!!!!!) to camp as much as possible.
If the Dedede has excellent perfect shield timing, then neither of ROB's projectiles will work, but even if they never hit, they always force Dedede to approach, which is how ROB wins this one.
I'll briefly address what happens if ROB approaches.
1. ROB attacks
2. Dedede doesn't get hit
3. ROB gets grabbed
4. ROB takes 60%
5. Dedede vs. ROB becomes 65:35 Dedede's favor, or more.
5. ?????
6. PROFIT!!
If anyone wants to disagree with that point, then go ahead, I'll be happy to debate.
If Dedede approaches (assume he has to):
Space as well as you can, with as many different moves as you can. Stay the F*** away from our grab, which really just means space perfectly all the time.
Spot dodge to Down Smash is good, HOWEVER, you absolutely HAVE to mix it up, because we can easily shield the entire thing then grab you. Change the timing slightly, and grab us as often as possible after you learn how to predict the individual Dedede's movements.
There are basically two main "stages" I see when I fight ROB. The first is the long-range fight, which simply involves the ROB spacing and projectile'ing, and the Dedede trying to get to the second stage.
The second stage is the close quarters fight, which involves a huge amount of prediction, at least when two players who know each other well go at it. This stage is all about ROB spot dodging, Down Smashing, grabbing, and Dedede just trying to get a grab. This stage doesn't last long, because as soon as either player gets a hit, it goes back to the first stage.
If Dedede gets a grab in either stage, ROB needs to have a plan to increase the difficulty of the chaingrab. If you use proper DI AND spam Jab/spot dodge/whatever's fastest in your arsenal, then ROB becomes VERY difficult to chaingrab. No matter what you do, a frame-perfect chaingrab is impossible to escape, but struggling is still vitally important.
If Dedede completes the chaingrab, you're likely to go off the stage, which starts a third stage of fighting.
The third stage is ALSO all about prediction, as it is with any edgeguard attempt. ROB does have an excellent recovery, but a good Dedede still has plenty of options for at least doing damage while you're off stage. If Dedede Forward Throw's you, use DI so that you fly at a very high angle. From there, use jumps or Up-B to go off the top of the screen until you're over the stage. Dedede doesn't have a strong vertical game, so being above him is relatively safe. If you are forced under the stage, it is almost always best to just go under the stage. The third stage is ROB's least favorite, because of Dedede's strong aerial game.
Endgame:
Dedede will go for the kill one of a few ways.
1. Up Tilt.
It's the best individual move in our arsenal, and kills you around 120% reliably. I don't know the exact numbers. Just space like crazy when you get to high percents.
2. Forward/Back Throw.
Fresh Forward Throw (at the end of an average stage, with good DI) kills you around 250%, 270% to be safe. You're all thinking "WTF, that's ridiculous, why would you even list that?? It's like saying Jab kills at 440%!!!1!1" I'm saying it because it'll happen. If you space like crazy, don't get gimped, and predict most everything we do, then you can live that long. It becomes totally relevent.
Fresh Back Throw (at the WRONG end of an average stage, with DI that makes you go almost horizontal) kills a little earlier, like 220-230%. Here I assume terrible DI because the DI you want to use for his Forward Throw is exactly the opposite for his Back Throw, so if you predict the Forward, you'll fly horizontally on the Back.
3. Other crap
Dedede can be unpredictable when it comes to killing. A random Forward Smash, slightly unpredictable Down Tilt, a Dededecide, or a stage spike can all kill at random times. There's not much I can say here. Good luck!
Stages:
I'm not too good with stage selection, so I can't tell you what works and what doesn't. I do know that Jungle Japes is one of my least favorite stages, so if you can pick that one, you might want to. I also know that Yoshi's Island and Pictochat are decent in theory because ROB can't go under the stage.
I probably didn't cover absolutely EVERYTHING about this matchup, so feel free to ask about anything specific.
SUMMARY:
Camp liek ur ub3rg4y, don't get grabbed, stay on the stage.
My opinion of the matchup:
55:45 or 50:50 in King Dedede's Favor.