well, i currently have 14 uploaded analyses, but at the time i was badged i only had about 5 -- the main reason that i was badged was that i was active in C&C and grammar checked a lot of analyses. as for how long it took...well, that isn't really a relative question. a badge shouldn't be something that you try hard to earn. if you put in adequate work for the site and are a helpful contributor, then you will be badged eventually. very few badgeholders who i knew were trying to earn their respective badge/badges. it usually just comes as a result of hard work. in fact, trying to hard to earn a badge can even hurt your chances at being nominated. keep in mind that hard work doesn't go unnoticed, and eventually hopefully it can happen. ^_^
edit: yeah i agree with zystral's general sentiments.