While the Demon looks quite terrifying, it suffers from a lack of speed and is in fact the slowest boss in Momodora III.
It will start the fight by going some steps towards the character and then smashing the ground with the hammer. The smash itself can cause damage and will also spawn two projectiles, which will fly in a ballistic path.
The hammer can only cause damage if the Bakrog Demon is smashing with it; when he's just holding it, the hammer is completely harmless. Touching the Demon will cause damage, but as long as you keep an eye on its movement you should be good to go.
Both shooting and swatting the living hell out of him in melee works, just be careful of its attacks and react to it walking forwards/backwards. Overall, this fight should be relatively easy.