Two-phase boost converter output capacitor selection
If you look at your last waveform, the output current is the average of that waveform. So the capacitor current is that same waveform offset such that the average is at zero. That is, half positive and half negative per triangular waveform period.

If the circuit is at 100% duty cycle at 100% load and for small ripple voltage, then approx:

C = (1/8) * i * dT / dV


i = current at 100% load
C = capacitance
dT = half period (pulse width of T1 or T2)
dV = ripple voltage (p-p)


For example, i = 1A; dT = 2us; dV allowable = 0.02V


C = (1/8) * 1 * 2e-6 / 0.02
=> C = 12.5e-6 or 12.5uF