Soul Stalker

There is a chance this will happen naturally just by nature of the RNG (meaning you just might not get a weapon shop before the first Elite opportunity). Personally, using my build in The Bound One (90G) that focuses on Shuriken and pierce and Force upgrades, I was able to take out an Elite with a single Shuriken that was upgraded once. One other thing that'll definitely help is buying a pet and having it with you, since it's extra damage on top of your one weapon.