I hold Panamanian and Chilean citizenships. My Australian visa is with the Panamanian passport but I want to book with Cathay Pacific, with a layover in Hong Kong. Panamanians need a transit visa, while Chileans do not. Can I make the transit in Hong Kong with the Chilean passport and then enter Australia with the Panamanian passport? I am traveling from the US (where I currently study and my student visa is on my Panamanian passport too).
Yes. There's nothing uncommon about this. On the way out, just show your Chilean passport to Cathay staff in the US. There's no immigration control when leaving, so they only care about ID and visa status at your destination and transit points.
On the way back, when leaving Australia, you'll have to show both passports to the airline, as your final destination is the US, and your US visa is in the Panama passport.