Story-related and unmissable. This trophy unlocks after you defeat the Blood-starved Beast boss, which is the boss of Old Yharnam, and will be the third boss that most players encounter. This boss is extremely quick-moving and can easily poison you, so it is recommended that you have antidotes set as your quick-select item throughout this fight (and try to have a full stock of 10 of them). Stay close to the boss and attack it from behind, and you should be OK.
Players will earn the "Chalice of Pthumeru" trophy at the same time as this trophy. See the following video guide: