To defeat the Xenomorph boss in Contra III: The Alien Wars:
Keep your distance and constantly move to avoid its attacks.
Focus your fire on the exposed head and vulnerable areas.
Watch out for its projectiles and dodge them by using quick movements.
Utilize the power-ups effectively, especially Spread or Homing missiles.
Use screen-clearing bombs if you find yourself overwhelmed.
Pay attention to its attack patterns and timing to anticipate its moves.
Stay persistent, maintain a steady stream of fire, and dodge effectively to whittle down its health and emerge victorious.