To face a boss, you must first defeat all gang members from each turf at least once before entering a Boss' turf. Also, you must defeat the bosses in the order below to enter Reihou High School.
Sawaguchi: Hanazo Second District (just before the second shopping arcade), and again at Marukaunsou Haisoko Higashiguchi (back gate of the warehouse after defeating Nishimura).
Kamijou and Yamamoto: Below Shintakaragawa (below the bridge after the 2nd town) & again at the sauna (after defeating Nishimura, Mochizuki, and Taira).
Nishimura: Marukaunsou Haisouko (inside the warehouse)
Mochizuki: Marukaunsou Haibiru Shoumenguchi (outside the tunnel)
Taira: Midorimachi Third District (just before the third shopping arcade)
Kinoshita: Hanazo Park (after defeating Taira)
Kobayashi: Kobayashi Sangyo Kojou (inside the factory, after defeating Kinoshita)
Kunio or Riki (only when playing a solo game): Kobayashi Sangyo Kojou Uradeguchi (back of the factory, just before the last shopping arcade)
Himada: Yumemichou Second District (after the sauna)
Gouda: Outside Reihou High School
Onizuka: Reihou School Gym
Gotai: Reihou Classroom Third Floor
Ryouichi and Ryouji (Billy and Jimmy Lee: The Double Dragon Twins): Reihou Classroom Top Floor
Yamada: Reihou Classroom Rooftop