Sol Divide: Sword of Darkness

Overview from MobyGames: 'Set against a medieval fantasy backdrop, Sol Divide is a 2D side-scrolling shooter that pits one or two players against a horde of flying enemies. There are three different characters that can be played as, each with their own weapon and fighting style. Various magic scrolls can be found by defeating enemies which allow the player to cast several different types of spells including lightning and fire.'

This was later ported to Sega Saturn and PS1, with the addition of an Original mode that is similar to the Extra round you get if you complete the game without continuing once.

Timestamps:
01:59 -- Story Mode (basically the entire first loop)
14:55 -- Extra Round