Crab Alley is optional and isn't required for that badge.
You don't have to do Colossus Boulevard in order to get to Krokotopia, but it's still a good idea to do it. The other streets, plus a few odds-and-ends that Professor Ambrose wants done, are needed to advance to the next world.
Do you have to beat crab alley to get three streets savior and do you have to beat all the roads to get to krokotopia?
nope crab alley do not require Three street savior badge, and u can earn Three street savior from doing all of the quests on Firecat Valley,Triston, and Cyclopes. :D And i'm not sure about be able to enter Krokotopia i can't remember. SORRY :?