Big goddess is nastiest around (8)
I believe the answer is:
titaness
'big goddess' is the definition.
'titaness' can be an answer for 'goddess' (I have seen 'Giant goddess ' mean 'titaness' so perhaps 'goddess' could also mean 'titaness'). I'm not sure about the 'big' bit.
'nastiest around' is the wordplay.
'around' is an anagram indicator.
'nastiest' anagrammed gives 'TITANESS'.
'is' acts as a link.
Can you help me to learn more?
(Other definitions for titaness that I've seen before include "Giant goddess" , "Rhea, for example" , "Powerful female" , "Giant woman" , "Phoebe, say" .)