there is no kanji-only phrase for rock climbing. You could say 岩登り and it's understandable, but the common phrase is the katakana ロッククライミング or simply クライミング
In Chinese, it's called 攀岩, which I think has a lovely over-complicated hanzi which would look great as a tattoo, especially as it fades over time.
Perhaps you would prefer a bit of a climbing pun: 石に齧りついている