Ike/Zelda/Ganon/Sonic/Pika/Pit all are harder on wifi. Wifi Ikes are scary.
-----------------------------------------
Falco on FD, if they're good, cheap, and know what to do, is Link's hardest MU. If Link can use platforms, catch Falco and not be CG>spiked through bombs, damage, stage saves, Falco's not too bad. That's a big if up there^.
Link has a few 'murder MUs' like DDD, MK, Falco, Wario, Olimar, and slightly less-so DK, Fox, ICs, and Kirby. Although winnable, if you CP a stage and the opponent CPs a good character for it, (FD-Falco, Brin-DK/Wario, RC-MK/Kirby, etc) Link has one h*ll of a challenge, the MUs get worse to like 20-80 or even 90-10.
I do okay vs Diddys, maybe I need to play more of them.
__________________
Link has no all around good CP stages except Norfair, which is usually banned. The over-all best legal stage for Link in my opinion is PS1, because it's the right size for stage control, supports approaching and camping, has platforms, and terrain. It's at least feasible to fight any character there. Some stages are better if you know the opponent but they might have a pocket DK or whoever for CPs.
CGers I take to Brinstar, Battlefield, maybe Lylat, and J Japes because the water saves you if you're CGed to the right (not vs ICs).
When out camping characters: FD, Picto, PS1, Halberd, Japes.
When Approaching: Brinstar, BF, maybe PS1/SV.
When out maneuvering: RC, PS1, maybe Delfino.
--------------
Frigate is a bad stage for Link but unless it's vs certain characters like ROB or MK, it's better than people assume. Link can space well and moving camp. The only bad element is the right side of the starting stage 'phase'.
-------------------
Someone said Link is bad because he can't be cheap. It's true, lol.