The further Millia chains her blockstrings, the more telegraphed her actions are going to be. As such, it's to your benefit to confirm as quickly as possible to retain the most options. 236S is generally safe on block, but is technically -1 so poor spacing can result in Millia being thrown.
Millia's jump cancelable normals can be used to create high/lows, since they can be jump canceled into Bad Moon. Notable normals for this purpose are 5K, 2S, and cl.S(1). (The low being a chain into 2S or 2D, or a cancel into Iron Savior) Even with a 5K or 2K preceding these buttons, if the opponent FDs Bad Moon can still reach. Millia can also use her jump cancelable normals to start an IAD mixup (under the cover of 236H or 214H) or to just reset pressure in general, but this requires Pin in order to properly check an opponent's options.
5K > 6H is a useful gatling against aggressive opponents. Canceling 6H(1) into Roll on counterhit yields a full combo in the corner, but if you're too close you're liable to get thrown instead.
Jump-Ins: Millia has a number of ways she can choose to jump in on a target. Generally, Millia will be doing this after one or two airdashes, which is assumed in the content below. When normally jumping in, she can typically only do one or two buttons. Varying your blockstrings and other mixups is vital in order to keep an opponent from feeling confident they can consistently block or escape your pressure. Example jump-ins, some are standing-only and require different confirms upon landing.
- j.KS x 214S
Be aware that the above all hit at slightly different timings. By omitting later portions of a string Millia can land early at any time in order to go low or try to grab. She can also make her first airdash empty and perform a second one while still being able to hit three overheads. It's important to vary timings in order to avoid opponents being able to fuzzy-block your mixups.
Air Combo > Pin > 6H x Secret Garden: Millia is technically minus, but has some applications.
Air Combo > j.H(N) x Pin: Best Secret Garden oki setups, but hard to setup.
Ground String > 2D x Secret Garden: Not applicable in all matchups, but sometimes a strong midscreen option.
Tips and Tricks
When Millia picks up her Pin, it makes the same "whoosh" as Tandem Top. You can use this to confirm if Millia was actually able to pick up Pin if it's partially offscreen or otherwise obscured.
Always be aware of when Millia has her Pin. Don't give up control of the ground it's on if you don't have to, but do be aware that the Millia player might be playing assuming they can't get it back. Don't scroll the screen if Pin is behind her if you don't have to, or if you have some benefit you can gain before you're forced to approach. (Ex. Setting Grinders, drawing Cards, etc.)