my friend is a pretty good samus player. zair is actually a really good tool to get through her missiles. since it also only has 10 frames of landing lag, its relatively safe. the goal here is to get samus in the air. her nair is one of the most annoying things ever for comboers, but luckily you have plenty of disjoint and three projectiles that combo. between bairs, nairs, uairs, and your projectiles, you shouldnt have a problem keeping her in your juggles. you just need to be careful to space your aerials, espcially things like fair, in order to try and avoid things like nair, dair, and bombs. you will definitely need to respect her airspace up close because of those things, but if you can bait her into doing one of those moves, she is relatively committed to it for awhile, and you can punish it easily. to get the kill, an up b is the only thing you are likely to combo into out of throws, but you can use your projectiles to set up for fairs and dairs. dont expect to combo zero to death though. youre going to have to be very patient with your follow ups and makes some reads on her actions in the air in order to get your hits. just keep chuggin out projectiles to cover her options and take the hits when youre sure of them. additionally, your attacks are very safe on her shield. cross ups will wreck any chance of an OOS nair or up b being effective, and you can also space your attacks relatively decently in front of her in order to stay out of range of those anyways. alternate between dashing away, continuing your jab sequences, and putting in dtilts even to try and poke and pop her up in the air. this will keep her guessing if youre going to be baiting out and OOS option or trying to drain her shield.
for recovery, mix up your AGTs, tethers, and up bs to avoid rockets and nairs. you have lots of good options over other characters to try and edge guard her, as your projectiles can cover tons of angles, and you can drop bombs to help cover the tether options. the back hit of nair is also great if she tethers too close, as a bair can be DIed up to live easily, whereas nair has a better angle.
overall i think that MU is in tinks favor, since he honestly out projectiles her and can cut out her airspace quite nicely.
the shiek MU will need patience in neutral, but i dont have too much experience with her with tink so i cant offer too much there.