Use mind games.
Grab more, counter more, cancel dancing blade+ smash, generally keep him guessing so he can't prepare the shield, wait to attack, and/or initiate a grab.
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MARTH IS NOT GAY, JOHNS!!!
MIND GAMES... every match needs mind games.
Steel2nd is right. You want to stay close enough to DK to never let him breath and essentially you want to beat him off the stage via Fair, Fsmash, SB, DB (neutral), DS, and even counter.
When you have him offstage it's easy pickin'... be wary he has 3 spikes... Fair, SideB, Dair...
Everything else seems situational.
For instance if you can get him to Up B (off stage) space yourself to Fsmash tip... if timed correctly you'll tip b4 he gets his invincibility frames from ledge grab. (don't ledge hog, since DK's lasts a helluva long time.
Make sure not to get the position to be grabbed when near the edge. As the others have already discussed--you will be stage spiked...
I'm not sure if Nair > DK'S Bair holds water... but just space and punish is really all...
PRESSURE. Don't play aggressive on big characters... they typically outrange you so you can't go around their attacks. Move first.