The term that comes to mind is 'meteorically eccentric'. The effectiveness of that, however, will depend upon your delivery; if it's written, delivery shouldn't be a problem, but if it's spoken, poise, skilled control of intonation, and timing, will all be central to the phrase's communicative value.
The original, 'batshit crazy', is not an especially worthwhile phrase to start. It relies primarily on shock value, which is undermined by its contemporary familiarity: 'batshit' only serves as an intensifier for 'crazy'. In literal senses, batshit is hugely important, and not at all crazy.
The most straightforward senses of 'meteorically' and 'eccentric' communicated by your phrase would of course be figurative, and because you alone know what you're describing (other than the general sense), it might well be that you could think of a more apt metaphor or simile.
Of 'meteorically eccentric', the nuanced oxymoronic play on literal and figurative senses bolsters the effect. The usual figurative use of meteoric to suggest a rapid rise (in career, reputation, etc.), will always be contradicted by the (literal) experience afforded by personal observations on earth, where meteors are known to fall.
Here is the sense of 'meteorically' intended:
Like a meteor; with the suddenness and speed of a meteor.
["meteorically, adv.". OED Online. September 2016. Oxford University Press. http://www.oed.com/view/Entry/117473?redirectedFrom=meteorically (accessed October 31, 2016).]
Of 'eccentric', figurative and literal senses should be simultaneously in play. The literal, loosely astronomical sense is provoked by the word being modified by another astronomical term ('meteorically'):
eccentric, adj. and n.
5. a. Of orbital motion: Not referable to a fixed centre of revolution; ....
b. transf. Of a heavenly body: Moving in an orbit deviating (more or less) from a circle.
6. fig. Regulated by no central control.
a. Of actions, movements, and things in general: Irregular, anomalous, proceeding by no known method, capricious.
b. Of persons and personal attributes: Deviating from usual methods, odd, whimsical.
["eccentric, adj. and n.". OED Online. September 2016. Oxford University Press. http://www.oed.com/view/Entry/59245?redirectedFrom=eccentric (accessed October 31, 2016).]
It should be noted that 'eccentricity', in figurative senses, is ambivalently appreciated. It does not, however, have a necessary relation to mental illness.