WordNet sense 1 (having complicated nutritional requirements; especially growing only in special artificial cultures):

exacting

WordNet sense 2 (characterized by excessive precision and attention to trivial details):

persnickety, pernickety

WordNet sense 3 (marked by extreme care in treatment of details):

meticulous

WordNet sense 4 (exacting especially about details):

finicky, fussy, particular, picky, finical

WordNet sense 5 (excessively fastidious and easily disgusted):

dainty, nice, overnice, squeamish