Yes you can get Brachydios gem from the village quest. I got two from him out of my 8 fights. I did brake his horn, both his hands, cut his tail, and capture him all those time too. --- Your face, it burns my eyes!
I have beaten him 6 times so far, 5 in the village 1 in the online urgent. So far, I've gotten 4 gems, 1 off a tail carve, 1 off a body carve, 2 off the village quest rewards, all my gems were gotten offline so far.