Calculating transfer function for complicated circuit
This circuit is a 7th-order system and if you apply the impedance divider as recommended, then you'll end up in a total algebraic paralysis unless you want to use a computer for doing it. If you want to derive by hand and express it in a readable polynomial format, the best is to apply the fast analytical circuits techniques or FACTs, they are unbeatable in passive circuits like the one you shown. I have published a book on the subject and an introductory seminar in 2016.
The principle is quite simple, you have to determine the time constants of the circuit in two conditions: with a zeroed excitation you obtain the poles of the circuit and when the response is nulled you determine the zeroes of the transfer function. By inspection for instance, I can see there are no zeroes in your circuit, only poles.
As an example, I have derived a 6th-order transfer function and the circuit was that one below:

There are no zeroes either in this one. So after zeroing the excitation (the voltage source is replaced by a short circuit), you temporarily remove each energy-storing element and determine the resistance \$R\$ &quot;seen&quot; from its terminals. That resistance is then combined to form the time constants you need: \$\tau=RC\$ and \$\tau=\frac{L}{R}\$. This is what is shown below:

What is cool is that you inspect the circuit and don't write a single line of algebra which avoids mistakes. The good thing is that you can come back to these little sketches later if you spot a mistake: just fix the guilty sketch without restarting from scratch. It saved me many times : )
As you go up in the terms, it becomes a bit more complicated but the principle remains the same: a sketch from which you can infer the time constants while the elements are either shorted or open-circuited:

Once done, you can use the method you want to determine the transfer function with a brute-force approach as a reference function. I personally favor Thévenin but you could use any other one. With Mathcad, there is no need to develop the expressions which is good:

Then, you can plot the response obtained from this approach and compare it with that given by the FACTs. As you can see, the format is already in an ordered form where all coefficients are individually determined:

If you carefully determined the time constants, then the error between the brute-force approach and the FACTs should be in the solver noise, in the pico range:

I obviously won't encourage you to go straight to solving a 6th or 7th-order circuit with the FACTs. But the method is truly an extraordinary tool and once you've acquired the skill, you won't go back to the classical method. Start with simple first-order circuits and increase complexity until you master the method. Then, you can jump on more complicated circuit as yours. Good luck!