My Singing Monsters
To Adjust Volume, select a Monster and press Move. From there, a bar will appear on the bottom left. By default, the volume is all the way at the top, but you can lower it by sliding it to the left. Sliding it to the very left will almost completely "mute" the monster, though the monster will continue to animate.
Dawn of Fire
To adjust volume in a monster, tap on the monster, press "Move" then adjust the volume settings. Adjusting volume to the very end mutes the monster, while adjusting very slightly right to the quietest part of the volume settings will make the monster super quiet.