You know the the sign that says no mining in the boss battle area(It is left from where you appear)? there is a sharp rock next to it that you can mine.
Mine the pointy rock, and if you have found the right one, it will fall on a button which will activate the drill car. But first you need to switch the tracks, so when the drill car is activated it will head for the ink bowl. Once you have done that, quickly connect the batteries to the sockets, grab the life crystal and stand on the platform.