Breaking shields should not be your priority when performing shield pressure (just look at how rare shield breaks are in competitive matches). You're mostly trying to either pressure the opponent into doing some sort of out of shield option and then punishing it (for example: you forward tilt their shield, they try to jump out or grab, you immediately do a second forward tilt to hit them out of it), or shield poke them and convert off of that. You are also trying to keep your opponent in a bad position where they are not able to threaten you as much (if they're shielding then they can't hit you or take control of space).
By mixing up the timings of your attacks on shield, you keep the opponent guessing about when they should be acting out of shield by threatening to hit them of their options; in order to cover certain options, they make themselves vulnerable to others. This allows you to get away with heavier/riskier (higher reward) interactions.
Generally, you should be spacing at the outer limit of your attack's range, and out of the range of the opponent's out of shield options (so that you don't get caught by shieldgrabs, aerials out of shield, etc).
The ability to do 2 aerials in one short hop, and just generally the amount of time you're in the air during a short hop, allows for decent mixups with aerials on shield. You can do things like mix up early dair/fair to immediate second dair/fair, or to various timings of nair, or to empty landing->something (such as a grab or down smash). You can also generally vary your timings a lot. You have the option of wavelanding out of high short hop aerials, which can be useful.
Cross-up wavedash up/down smash will make you slide extremely far away if it hits on the opposite side of their shield, making it very safe though difficult to directly follow up on. This wouldn't really be something that you'd try to pressure a shield with (more a way of fishing for a combo or kill in neutral), but if the opponent happens to shield it then it's somewhat safe.
Using grabs is a important aspect of pressuring shields, since they stop the opponent from just sitting in shield until you have to stop hitting them.
Without having much PM Luigi experience (and with most of it being in 3.02 before the nerf): Cyclone is good if you hit them relatively early in the animation since you can rise as you hit the shield and then combo straight into a nair (or fade away/retreat). If you end up hitting the opponent out of their shield or otherwise hitconfirming then you can do a pretty serious combo from the tornado since it doesn't send them very far.