Until you get into the really mind-bending stuff in Bloodborne, most of the game's areas are shockingly closely-packed. And in fact, some areas that feel huge (usually due to the large density of deadly enemies) actually wind up being pretty small if you actually look at them. I also find it pretty ironic that "Central Yharnam" isn't really the "hub" area - Cathedral Ward clearly is.
Anyway, after wiping a couple times (one after maybe twenty seconds) to Vicar Amelia, I had the notion to go to Hemwick. Hemwick and the Nightmare Frontier are both right off the path up to the Grand Cathedral, though the paths are rather tricky to spot if you're running from church giants.
Hemwick was an area I used to use a lot to farm Echoes on my first run, and it really isn't a very hard place to get through. In fact, I'd argue that it's probably the easiest stretch of the game.
There are enough Twin Bloodstone Shards in Hemwick you can find here to upgrade a weapon twice (I'm using the Threaded Cane at the moment, though I think I missed the Powderkeg badge, which I think is in Old Yharnam but I could be wrong.) This, coupled with the ability to use Caryl Runes after killing the Witch(es) of Hemwick (that can't be a Witches of Eastwick reference, can it?) really improves your chances on Amelia if you go here first.
Once again, I one-shot the Witches, though there was a scary moment in there when I started to get swarmed by the adds. At this point I think that I'll be embarrassed if I ever die on that fight. We'll have to see how things go with Shadows of Yharnam, Amygdala, and... well, Mergo's Wet Nurse, Gerhman and the Moon Presence, though I don't really count those as I was super-leveled up to take out the Orphan of Kos before I fought them.
Anyway, with +5 Threaded Cane in hand and a couple modest Caryl Runes imbuing my brain with some bonuses, I came back and fought Vicar Amelia again, and this time things were a lot easier. I managed to stagger her and do a couple of visceral attacks, including the killing blow, which felt pretty satisfying. Too bad I won't hear that awesome Cleric Beast/Vicar Amelia boss music until I get to Laurence (or start working on New Game + with my original character.)
Anyway, I think that any subsequent run will have me heading off to Hemwick as soon as I can, as it's a lot smoother of a difficulty curve than going straight from Bloodstarved Beast to Amelia.