Barnes 85grain TSX, will perform as a heavier bullet, will punch thru the shoulder given reasonable distance 200 yards or less, accurate, you wont flinch with a 243 so you can put it where it needs to be.
once you hit him, keep fireing, they can soak up a lot of lead and poor blood trails due to hair. Kepp shot distance reasonable, wait for broadside and you will be fine.
Life is Short; Live, love, Hunt
270 Winchester.......Jack had it right