Context is essential for a decent, meaningful translation. Nonetheless, I'll try to give some generalities.
She's got what it takes means that she has the necessary attributes to do something. Example: A difficult task needs to be done. It requires intelligence and determination. To say, 'She's got what it takes.' simply indicates that she has both of the necessary characteristics to accomplish the task.
I've got you under my skin: I am preoccupied by you--generally in the sense of liking someone very much, thinking about them all the time.
Perhaps I should add that for she's got what it takes, there can be a BUT, i.e. BUT still it doesn't mean that she can necessarily complete the task well. (for example the objective circumstances are against her, etc.)
But as Benjy always says, I could be wrong and I'll go now.