There are a lot of shortcuts in going to the rooms in Mudha dungeon, some still might not be discovered. Here are the few that I know of.
1. Cali's room - use Exile portal to warp to Mantra Temple. walk towards the Indra portal then use the Baruna's flute.
2. Chandi Naga - use Mandara portal to warp to Mara land then use Baruna's flute from there.
3. Chandi Asura - from Jina portal, warp to Rest place then use the Baruna's flute.
4. Golems - use the Baruna's flute infront of the Biryu Commercial area portal
5. South Byulnak - from Exile, warp to Mantra temple. walk towards Indra portal then use it to warp back to Mantra. Use Baruna's flute from there.