React badly on Philistine's becoming artistic (8)
I believe the answer is:
creative
'artistic' is the definition.
(I've seen this before)
'react badly on philistine's' is the wordplay.
'badly' indicates an anagram.
'on' is a charade indicator (letters next to each other).
'philistine's' becomes 'I've' (where the crossword setter is 'Philistine').
'react' with letters rearranged gives 'creat'.
'creat'+'ive'='CREATIVE'
'becoming' acts as a link.
(Other definitions for creative that I've seen before include "Full of ideas" , "Having the power to be original" , "Innovative in reactive way" , "Inventive, artistic" , "Reactive in artistic manner" .)