Proceed with difficulty, having wilted (4)
I believe the answer is:
limp
This clue might be a double definition.
'proceed with difficulty' is the first definition.
'limp' can be an answer for 'proceed' (limping is a kind of proceeding). I'm not sure about the 'with difficulty' bit.
'wilted' is the second definition.
(synonyms)
'having' is the link.
Can you help me to learn more?
(Other definitions for limp that I've seen before include "Walk with an uneven step" , "Flaccid" , "loose" , "Saggy and drooping" , "Slack, wilted" .)