Climbing / climbing - what is the right way? The word "climb" is a colloquial word.
There is no such form in the literary language. It is sometimes used colloquially or in fiction to convey an informal style, the speech of a child or person speaking illiterately. But the corresponding literary variations are "to climb" (imperfect) and "to climb" (perfect).
Therefore, in writing, in formal speaking, and in general - when you want to speak competently - it is better to use "form". Grammar of Russian proverbs