Big Band: I think that this one is slightly on Eliza's favour . She can get through Giant Step HK with her cr HK, she can punish almost everything Band can throw at her with sekhmet and she has the best armor in the game, which is one of Big Band best strength point. Also, she can mix up him with ease thanks to his height, jumping, calling servants and using sekhmet.
Cerebella: This one I feel it's even, or slighly in Eliza's favour. Not sure why though, I kinda feel that Eliza has loads of options to get through Bella defence, and can easilly avoid to enter into the grab range.
Parasoul: Dunno this one, I still have to play against a good Parasoul to grasp the matchup info, for now I'd say in Eliza's favour, even if those mix ups can be scary.
Peacock: This one is on Eliza's Favour. She can use her cr HK to get near, get peacock with Weight of Anubis while she is throwing things, she can get through everything with sekhmet (even though she gets a lot of damage) and mostly, if Peacock gets into the corner is likely dead meat. Getting near her can be quite boring since you'll have to run, boat, try to punish, defend more than once, but that is the same with every character, the difference is made primarly by cr HK since it allows to get near faster and, if in the right range, punish even the Argus Agony with upperkat.
Painwheel: This one... I feel like it's even or slightly in Painwheel Favour. Eliza is doing fine against painwheel and has good options, but the lack of a "normal" dp is a nice thing for Painwheel, since she can expect to be able to pressure all the time without being caught by upperkat into her operative range (close). The key should be to keep painwheel into the mid range, so she can be dp with upperkat.
Fillia: Same as Painwheel. The only difference here is that updo weakens Eliza's offensive air options, jump hp is quite risky to use and that airdash is quite nasty.
Fukua: In favour of Eliza. Her "Zoning" game with bubbles is weak against eliza's cr HK and sekhmet. And Fukua is also slow and has to come near to be a threat, so she has to get into the mid range which is Eliza's forte.
Squigly: Even. She can pressure fine if charged, but she can have some troubles with Eliza midscreen range. Squigly isn't comfortable while charging since she has to avoid weight of anubis, but can pressure Eliza with j hp that has a nice range, and more important she can pressure Eliza using center stage + super to get near into the "comfortable" range to mix up.
Valentine: Even though I haven't played much against Valentine, I'd say it's in favour of Eliza. Val has a nice ground dash and solid tools, but eliza beats her in everything else. And the lack of a reversal is good since Eliza can pressure all the time calling servants whenever she get pushblocked without being punished (at max you'll get a sting)
Fortune: Dunno this one, I have yet to play against a good Fortune, for now I'll say it's mostly even since the both excell where the other one is weak (Close range Fortune, Mid Range Eliza).