hmmm, just use nodal analysis. You will get a system of equations which you can solve for
the output (voutp-voutm) and divide by the input (vinp-vinm) in order to obtain the transfer
function.

Hi

You can easily derive it by finding using thevenin equivalent circuits. You can use the concept of hemi-circuit, based on the fact you are analyzing a fully diff (purely symmetrical circuit).
If you split the input circuit (Z1/Z3/Z1), you'll get a simple resistor divider equal to Z3/2÷(Z3/2+Z1). That is the input impedance of your input voltage source.
Z2 does not play a role in the transfer function assuming the op amp's input impedance is >> Z2.

From this you get H=-(Z4*(Z3/2 + Z1)) / (Z3/2)

Hope this helps
Tosei