How to regulate a 3.6 V battery to two power rails (3.3 V and 1.8 V)?
My load current for the 3.3 V rail is 546.2 mA. My load current for the 1.8 V rail is 1.154 mA.


Your 1.8V rail is basically just a reference voltage. A voltage divider from a regulated source would work just fine. A 1.8V 1.154 mA load is like a 1500kΩ load, keep that in mind when you make your voltage divider. Efficiency isn't really an issue here. Even at 50% efficiency, that's 4mW.

As for the 3.3V rail, with a 3.6V  battery, likely a lithium battery, you want a buck-boost switching regulator, as the voltage range of the battery will be above AND below 3.3V. You want it to regulate down, and then regulate up. Look for one based on your battery chemistry, as there are some that have built in battery protection, to prevent it from draining too low.