Cowboy Bebop

Summary (source: IGDB)

The player controls Spike Spiegel's Swordfish II from a third person perspective. Each level involves chasing another ship (the bounty head) along a set track through different environments, while enemies (spaceships, robots, etc.) attack. Each stage ends with a boss battle, confronting your target. Between stages, bonus points earned can be spent to purchase upgrades for the ship (faster speed, more powerful ammo, stronger laser).