I've been playing only Mileena for 95% of the time the past few weeks and here are her worst match-ups from bad to terrible:
Jade: 5.5 : 4.5 - She negates all forms of sais with shadows on reaction and there's nothing you can do to prevent her from getting mid-screen. Mid-screen she's dumb, you have to deal with her U+3 all day and there's nothing you can do about it besides random rolls and teleport drops which is more harm than good.
Shang Tsung: 5.5 : 4.5 - His ground skull makes it so you can't use sais at him without risk of being popped up, you have to constantly rush him down and do a ton of random teleport kicks to stop him from controlling the match. With Mileena's slow normals and Shang's pressure up close always leaving him at an advantage it's tough to get anything going.
Nightwolf: 6 : 4 - Nightwolf's reflector shuts down ground sais and his shoulder shuts down air sais, so you have to play a grounded mid-screen game. His F+3 normal goes over and crushes Mileena's D+4 and makes you never want to throw it out in risk of eating 40% just for a 3% poke.
Smoke: 6 : 4 - Smoke shuts down ground sais with his shake and can punish air sais with teleport on reaction. He can turtle while building meter with his teleports and smoke bombs. Smoke bomb also stuffs teleport drop since Mileena goes into the ground before teleporting. Overall he's just annoying and Mileena struggles when she's forced to constantly rushdown with random teleport drops and her slow normals.
Kano: 6 : 4 - It's really tough to punish Kano's up ball on reaction, sometimes it's so strict I don't even attempt to go for a roll since the risk is him recovering in time and then counter punishing me. He can throw knives purposely when you throw sais and always win the trade since Mileena's sais do 6% and Kano's knives do 9%.
Raiden: 7 : 3 - This match is just stupid, you're forced to sit their and block or jump around like a maniac. I like to switch between the two but overall there isn't much you can do since Raiden can counter just about everything you do on reaction. His vicinity traps work on Mileena so it's hell if you're ever stuck in frame traps and he just controls the match way too much for you to ever get a momentum started.
Kung Lao: 8 : 2 - It's like Kung Lao was designed to rape Mileena. He has every damn tool in the book that counters anything she can do, just a pointless match up to even consider playing through, IMO. His F+3 goes under air sais and he can hit confirm into spins for combos, dive kicks beat ground sais, teleports just give him to many options that EVEN when you know he is teleporting you have to guess if he's going to do an instant 3 then be left at advantage or 2 and many other specifics. Spin punishes ANYTHING she does (even counters D+4 range), including her enhanced teleport drop. So you are stuck playing defensive in block while he builds meter constantly chipping you to death and crossing you up. Once he has x-ray just put the controller down because you aren't doing shit.
I can go into way more depth about these chars but just wanted to make it as breif and straight to the point as possible. Considering some of these chars are very popular in tourneys you would see why you would need back-up chars to fight some of them. And if anyone wants to know what I used to come up with some of the match-up info it's from playing people who use a certain char really good from playing both off-line and online.