The second stage isn't a proper LPF either, the gain at high frequencies approaches 1, not 0.
Assuming ideal opamp, the frequency response functions would be:
\[G_1=\frac{1}{1+j\omega R_1 C_1}\]
\[G_2=1+\frac{R_3}{R_2(1+j\omega R_3 C_2)}\]
\[G_3=\frac{1}{1+j\omega R_4 C_3}\]
\[G=G_1\cdot G_2\cdot G_3\]
To draw a Bode plot by hand, you first draw the response of each individual filter segment (simple straight line approximations are fine) and then add the responses together for the response of the whole circuit. It is a simple matter of adding the gain responses together (loglog scale, of course) and adding the phase shifts together (linlog scale).
I could go in detail about how to draw the individual reponses, but
this site does a way better job at explaining it.