She's one of the most difficult people I've known as far as typing goes. For every type, there's something that doesn't fit. These are the types that have more than a 2% chance of being her type though, imo.

SLE
EIE
LSI
LIE
SEE
ESI
IEE

Some of these types are more likely than others, but like I said, it's only a list of the types that there's more than a 2% chance she is.