Mrs. GREEN APPLE's "シンデレラ" (Cinderella) is a fairy-tale title on a song that is mostly a confession. The singer opens by asking herself "こんな処まで なにをしにきたんだっけ?" (what did I come all the way here to do again?) and admits the tears are already falling. Then she begs for reassurance: "ねぇ そうだよね? 答えて お願い" (hey, that's right, isn't it? answer me, please).
The chorus is wonderfully blunt. "いつだって 私がシンデレラ" (I'm always the Cinderella) is the fantasy, and straight after it she shrugs: "叶うはずないもの" (it's not like it could ever come true). She calls herself a liar, greedy, a coward, and someone who envies everyone, and keeps landing on "これが私だもん" (this is just who I am). That little もん at the end is a casual, slightly sulky way to give a reason, the way a kid says "because!" It makes the whole line sound defensive rather than proud.
The image I love most is "既に器はヒビ割れてる模様です" (it seems my vessel is already cracked). A 器 is a bowl or container, and in Japanese it is also a common way to talk about a person's capacity or character, so she is saying she is breaking under the effort of trying to be loved. The polite 模様です (it appears that) makes it sound like a weather report about her own heart, which is darkly funny.
She lists exactly who she wants to be: "愛されるあの子" (that girl who is loved), "純粋なあの子" (that pure girl), "裕福なあの子" (that rich girl). Watch the wordplay too: early on she says the dream 叶う (comes true) is impossible, and later that she can never 敵う (measure up to) those girls. Both are read kanau, so the song swaps "come true" for "compete with" without changing the sound.
By the end she flips it: "この痛みこそが とても私だもん" (this pain, more than anything, is so very me), and "唯一のシンデレラ" (the one and only Cinderella). She doesn't get the glass slipper. She decides her own messy, jealous self is the main character anyway, at least "世界と死ぬまでは" (until I die along with the world). It's a bit much, and that's the point.