A shutter chance is achieved when the enemy is on the verge of an attack. The charge ring converts from yellow to red to signify that the enemy is about to attack, and that its time to take a photo. Shutter chances deal more damage than a regular photos, and if done at the right time, could result in a Fatal Frame shot.
In Fatal Frame V, aside from the previous method, each ghost and allied character now has specific spots that can be targeted (e.g: Shino Kururugi's spots are her head, noose and knees), and Spirit Fragments that detach when taking damage before returning to the enemy and restoring health, and that can also be targeted. If there are at least five targets within the capture circle, this will also provide a stutter chance.
Unlike the former method, the latter does not lead to Fatal Frame shots but will still inflict significant damage and will stagger enemies.