I could do it. Would it be my first choice? No. But in an emergency I could do it with a .22LR. Heck the greatest of the original Great White Hunters on the African continent in the late 19th century was a guy named Karamojo Bell. He regularly took elephant with a 6mm. That's a .243 folks. Shot 'em right thru the eye everytime. The importance of shot placement is shown once again.
Our school library had "Karamojo Safari" and I read it in high school. Have read quite a bit about him since.
Bell primarily used the 6.5 Mannlicher Schoenauer (unsure of the spelling) and .275 Rigby (7mm Mauser). He used the long parallel sided round nose fmj bullets because he thought penetration was the most important thing in killing elephants and other large game.
I have some of those old type bullets in 6.5 Swedish Mauser and their penetration is astounding. They will shoot right through a large (very large) tree trunk.
The graveyards are full of what remains of Karamojo wanna-bes.
Placement and adequate penetration were his guiding principles.