The Volcano is one of the many traditions of Gradius, and as such is one of the most recurring Sub-Bosses in the series, originally appearing as the Stage 1 Sub-Boss in Gradius.
Whilst they mainly appear mid-level, often they will appear directly before the boss, and has at one point actually been a stage "boss", such as in Gradius 2 Famicom where two of them directly facing each other, is the last thing encountered in Stage 3, and can even be destroyed, in a manner of speaking.
As part of the tradition, when faced as a Sub Boss it is usually accompanied by the theme music: Aircraft Carrier.
The Volcanos erupt, as one would expect, and send a somewhat ridiculous number of rocks hurtling into the sky in a random direction. Depending on the volcanos' position, the rocks will then fall to the ground or ceiling.
There are two main working strategies that can be put to use:
Either stay at the top left of the screen, releasing the odd missile or shot when a stray long range rock comes your way, or stay directly positioned at the top of the volcano and destroy the rocks as they come out.
The latter is usually only viable when you have multiple options and a laser.