Tsundere
"In Japanese, there’s a phrase called 'tsundere,' which means in the beginning you’re kind of snobby and cruel, but towards the end your shell kind of breaks off and you become sort of sappy."
— Eiji Aonuma, speaking with GameInformer
The Japanese word 'tsundere' is a portmanteau of the words 'tsuntsun' (meaning "aloof" or "cranky") and 'deredere' (meaning "lovestruck")[1]. It is used to describe a character type which fluctuates between emotional extremes, and is frequently applied to characters who appear initially to be aloof, dismissive or teasing, and through character development are revealed to be less apathetic or more caring.
As the quote from Eiji Aonuma implies, Midna exemplifies this character type. Throughout Twilight Princess she undergoes a character evolution which showcases her 'tsuntsun' and 'deredere' duality, both through her relationships with Link and Zelda, and her attitude towards Hyrule.
Although Midna, when Link first meets her, is teasing to the point of abrasiveness, through careful character development she is convincingly shown to warm to him without losing the teasing, slightly sarcastic side to herself — although becoming more good-natured in it. Zelda implies in her line about Midna's self-sacrifice that her apathy towards the state of Hyrule masks a desire to save Hyrule as well as the Twilight Realm — a desire which Midna may or may not acknowledge, but which she goes on to vocalise when Zelda sacrifices her power to save Midna's life. Midna also belies a desire to see the Hylians well in her line at the end of the game expressing hope that they are mostly like Zelda, with a good heart, and will "be okay".
Although 'tsundere' is stereotyped as a character who swings violently from outright hostility to sappy affection, Midna is more moderate in this quality; she fluctuates between teasing sarcasm and affectionate sentimentality, although she can fly into a passion when angered — as demonstrated when she defeated Zant using the power of the Fused Shadows. It is not so much that her sarcasm is a façade, but that these are two sides of her personality which come into play depending on the circumstance.