I play against my brother's secondary Pikachu (which admittedly isn't amazing but then again, I'm not either) and on paper, the match-up seems very bad; Pikachu has very good, very flexible recovery, can play keep-away with thunder jolt and his superior speed, and can combo Jigglypuff surprisingly well. It's definitely a losing matchup in my opinion. Pikachu is simply a better character, he's fast and safe, and sets up his vortex that can be very hard to get out of.
We can take advantage of his lack of killing power and light weight in the ways you may expect. His safety makes it hard to punish with Rest, but if you can find holes in your opponent's pressure, by all means go for it. Since his moves have no range, he will be very close to you during strings, and it's possible you may be able to get a Rest out of shield that can easily even the odds. Quick Attack is very safe, but I think nair can clank with it, if not beat it. I need to actually test this out... x_x
Pikachu will likely be looking for grabs, shooting thunder jolts off in neutral and chasing them if you shield, or just Quick Attacking into you followed by crossup up tilt into big damage at low percent. It's easy to get stuck in the blender if you get opened up, so maybe stay airborne? I'm still trying to figure this out myself. Nair and fair beat his projectiles, so patient play is possible. It's not like Toon Link, where you basically need to approach.
This is just my rambling thoughts thus far. I obviously have a lot to learn about the Pika v Jiggs MU, but it doesn't seem very good. Doable? Probably.