"This woman is not bad."
Translation:यह औरत बुरी नहीं है।
Yes. It is necessary.
As you may know, है is optional in most present tense sentences that contain नहीं.
However, if we remove है from this particular sentence, the sentence will have no verb which is not allowed. So, you can't remove the है in such sentences with no other verb.
नहीं should be placed adjacent to a verb. It is usually placed before the verb but can also be placed after the verb (except in the case of auxiliary verbs like है, रहा etc. for which नहीं should always come before).
The only verb in 'यह औरत बुरी नहीं है' is है (because बुरी is an adjective). So, नहीं should come before है.
Note: Most of these rules pertaining to word order are only followed in formal and written Hindi. Colloquial Hindi is very flexible with word order.