Highpass filter design that is better than the Moving Difference filter
[ 0.25      -0.6035         0.25       0.1035] seems to work.
Here is how I did that: Since the &quot;breakeven point&quot; is specified at $pi/2$, we know that $|K(0)|^2 = 0$, $|K(\pi/2)|^2 = 0.5$ , and $|K(\pi)|^2 = 1$ . The magnitude of the spectrum is thus given at 4 different points. DC and Nyquist are real and we have a conjugate complex pair at $\omega = pi/2$. We can use this to populate a 4 point frequency domain vector and perform an inverse FFT to get a 4 tab impulse response.
The only thing we don't know is the phase at $\omega = pi/2$. A highpass filter generally has a falling phase and the phase should be zero at Nyquist. Hence we should interpret the phase at DC to be 180 degrees and so it's reasonable to guess the phase at $\omega = pi/2$ half way in between and, $\phi = -pi/2$ seems like a reasonable first guess.
y = ifft([0 .707i 1 -.707i].');

You can play around with the phase and see if it can be made better (whatever that means), but given the amplitude constraints, any 4-tab solution must more or less look this way in the frequency domain.
EDIT
Turns out a phase of 75 degrees gives optimum performance in a sense that it both maximizes the gain at $\omega =3pi/4$ and minimizes the gain at $\omega =\pi/4$