See daughter rib lying participants, in a dreadful manner (8)
I believe the answer is:
terribly
'in a dreadful manner' is the definition.
(I've seen this before)
'see daughter rib lying participants' is the wordplay.
'participants' indicates the answer is hidden within the clue (some letters 'participating' in the clue).
'TERRIBLY' can be found hidden inside 'see daughter rib lying'.
(Other definitions for terribly that I've seen before include "In a dreadful manner" , "Very badly" , "In an awful manner" , "Awfully, frightfully" .)