Can climbing it make you breathe badly? (4)

I believe the answer is:
hill
'can climbing' is the definition.
The definition and answer can be both man-made objects as well as being singular nouns.
Maybe there's a link between them I don't understand?
'it make you breathe badly?' is the wordplay.
I cannot quite understand how this works, but
'badly?' could be 'ill' ('ill' can be adverbial as in 'ill-advised') and 'ill' is present in the answer.
A single letter 'h' remains which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for hill that I've seen before include "Canvasser of opinions" , "Mount" , "Raised area of land" , "See 14" , "See 8" .)
