Falco can wreck Jiggs if you keep pressuring him with lasers. If he gets above the lasers, do not keep lasering. Your lasers will be too low, and he will just float right over them and bust you in the chin. If he goes above your lasers, either dash dance and see what he does, or charge him with a full jump nair. Falco's jump is so fast that he won't have time to react, and the only way you'll get hit is if he knows this is coming and starts a fair before you jump. That is why you sometimes dash dance, to throw him off.
If you pressure a Jiggs into their shield, you should shl towards them, stop right in front of them, just out of their shield range, and see what they do. If you are consistently approaching with shl to grab or pillar, and if you are not getting shield grabbed, their only options are to get grabbed, get pillared, or roll. If the try to jump out of shield, the laser will stun their shield long enough for you to be able to pwn them.
Now, if they roll, since you stopped in front of them you should be able to chase them. More than likely they will try and roll behind, and if they do, turn around laser to whatever you want. If they roll away, just continue your laser approach.
If the Jiggs starts charging the neutral b, just jump to a platform, if there are any, and then mindgame him into releasing it by running off the ledge then jumping, or any combination where you approach the floor, but then jump away before landing. If you don't have platforms, laser him. And if he is barreling towards you, just shield. You can shield 2 hits of it, then jump out of shield, and you'll be fine, because by the time you land after jumping out of your shield, rollout will be over.
I can not emphasize this enough: spike Jiggs with the dair. Jiggs can not sweet spot the edge without either doing rollout (which means you just jump out and get hit by it, and the Jiggs will spin to her doom) or sing. Sing is extremely risky for a Jiggs to do, because it is relatively hard to sweet spot with it (coming from below the stage). If they try to do the stall, and come above the stage with the sing, then you dair them to oblivion.
If they try to go high above you, utilize Falco's jumps (the highest jumps in the game) to position yourself above the Jiggs for a dair, or just mindgame them into attacking first, then bust her in the lip.
If you get off of the ledge, try not to up b, as you are basically helpless now. Your best bet is to sweet spot the over b, or go above the Jiggs with the over b. you just have to continually mix it up, because Falco's recovery gets ***** by Jiggs.
Don't miss l-cancels, or you're getting rested.
Learn to DI, or you're getting rested.
You have to be patient when fighting Jiggs, because all of your hard work can go down the drain with one rest.