How to increase current output of capacitor bank with buck booster?
The energy you want to deliver to your Arduino is

$$300\ {\rm mA}\times 5 \ {\rm V} \times 30\ {\rm s} = 45\ {\rm J}$$

The energy stored in your capacitor is

$$\frac{1}{2}\left(0.1\ {\rm F}\right)\left(5\ {\rm V}\right)^2 = 1.25\ {\rm J}$$

Of which you will lose some to inefficiency of the buck-boost converter, and some of which you will lose because you won't be able to drain the capacitor completely before the converter stops working. 

You need more the 36 times more capacitance to have enough energy to power your load, or you need to charge your capacitor to a higher initial voltage (30 V or more), if it can take it.

Or you could choose a different microcontroller that can operate on much lower current. A microcontroller alone can be found operating on a fraction of a milliamp. The total current needed by your circuit will depend on what peripherals you need to attach to it.