How to beat Dragon Skull thing (Responsibility)?

Pick up the green plants on the map. Specifically, the one the looks a like bush growing a gem. After picking one up, throw it into one of its nostrils. Do the same for the other nostril. Once you have done both, the boss will open its mouth and the weak-point shall be revealed.

For those who are lazy to read.
1. Pick up green plant with gems
2. Throw into nostril to jam it
3. Attack weak point immidiately
4. [Repeat]

Note: It is suggested that you kill the claw before you jam the second nostril since the sand makes you take more turns per move/attack. This will make the boss use a move that inflicts lots of damage on the map which will most likely kill Mana and Kyoya if they are in the AoE.