The correct answer is the first option - We all wanted to win so badly that we were practically willing the ball through the hoop.
You should write 'badly' and not 'bad' because you need to use the adverb rather than the adjective to modify the verb 'to win.' To use the adjective 'bad' here is really colloquial (and grammatically incorrect) so it cannot be used in formal writing, but rather only in informal speech.
