Honestly, the key to the Mario MU, in my opinion, is patience. Rushing in at him is almost a surefire way to go right into his UTilt combo, which is pretty bad for us since we're so big, it means we get stuck there for longer than other characters. But Flamethrower can be a pretty useful tool, and Mario can't use his Cape to reflect it too well; since it's a continuous projectile, he'll still get hit regardless. It cancels out his Fireballs, too.
However, Mario has some issues with recovering, which is what we need to exploit to win this MU. Pressure him offstage and play some mindgames on him; since Mario's recovery isn't the best, playing mindgames such as going for a spike and not actually spiking can spook Mario into doing something he shouldn't, like airdodging or throwing out a UAir. From there, you can either actually drop down and spike him or go back onstage as Mario falls to his doom. If you suspect he'll use the Cape on you, go for a BAir; if Mario does go for the cape, he'll only be delivering a BAir to himself. Keeping Mario offstage is important in the MU. Bait out FAirs and punish them. Fly OOS is a powerful punish against Mario, since he needs to get close to get consistent damage.
But whatever we do, DO NOT USE FLARE BLITZ AGAINST HIM. At least not to get onstage; any Mario worth his salt will use the Cape to turn us right around and cause us to lose a stock. If we need to use Flare Blitz, use it above the stage, where it's more unlikely for Mario to be able to use the Cape on us. Rock Smash is a good approach option from the air, as is FAir. Just keep pressuring Mario offstage and the MU becomes easier.