Bouldergeist looks like a bunch of rocks stacked together into a stone column. However, its true form is in actuality a small black ghost with a red bubble underneath it (possibly its uvula).
Super Mario Galaxy
In order to defeat it, Mario must use Bomb Boos to break apart Bouldergeist's rocky exterior and hit its red bubble with another Bomb Boo.
When Bouldergeist shapes two rock hands, some of its attack patterns are similar to Eyerok, another Mario boss. These hands can be tricky to avoid. When Bouldergeist raises its two hands, run away from under them to avoid being flattened. If Bouldergeist forms its hands into fists, move away from the two punches it'll (try to) throw at you. This boss's hands can also easily block the Bomb Boos the player uses. If you must, you can destroy the hands with Bomb Boos, though after a period of time Bouldergeist's hands will grow back.
After you destroyed him once, you'd have to do so once more in order to get 120 stars, though the second time would require you to do so without getting attacked once.