Shoot lasers from afar, and abuse mobility.
When closer, punish attempts to advance forward with shffl aerials and ftilt.
Watch out for desync walls.
Try to just wait for ICs to attempt something and put them in the air or separate them when they give you the opportunity. In akward closeups, grab (ideally Popo) and fthrow or dthrow to hit the other climber. Space/fade away dair into punish spotdodge or roll, or if they do anything else, dtilt (unless they get close enough to grab and can shield).
If they're not representing wavesmashes or ftilts, spam AC bair and don't move toward much if at all with it. When they whiff their punish on it, if they try, utilt them or shine them or fsmash them, based on what will hit.
Spaced fsmash can also mess with spotdodge desync attempts and shield grabs, but try to avoid doing this without exerting some other form of pressure first unless you're supremely confident in your spacing and positioning (and have it guaranteed in your mind they aren't about to move back or blizzard).
When separated, hit whatever climber you know you can, and try to do things that do damage, keep you in control, and keep them separated.
If you hit one climber and the other is too near for you to do certain combo options, feel free to grab the one you didn't hit and even throw them back into eachother, as long as you can maintain control.
If grabbing either climber when they're close together, dthrow and fthrow are usually the best throws, but bthrow when they're on opposite sides can be useful.
Try to do aerials around desyncs if you can or strike in the gaps. Don't be afraid to shield desyncs, but be ready to roll if they go for a grab.
Basically you can outcamp them, but if you get get close... Do safe stuff or wait, hit at least one climber, and if you hit Nana, grab Popo. If you hit Popo, hit Nana hard, but quickly. When both are separated, try to maintain control, and if you see a KO opportunity you know you can get, take it unless the other climber is capable of killing you for it. Abuse their massive shield knockback, but don't actively try to pressure so much as punish attempts to do stuff after a safe hit. Play a waiting game. Dash back is the best thing to do after a safe hit that's in range, but not a frame window for retaliation. Wall them out. Dair and dtilt both help vs CC and shield.