Help for a beginner

If you can, would you mind helping me? (with no spoiler if possibile)

I really don't understand what to do after the first big boss fight with the Horse looking robot.

I talked to the floating chubby cat and he gave me the bow (really cool animation)

I basically looked everywhere but I can't seem to find anything except dead ends.

I probably am either really stupid or really blind but please have mercy.

(The only thing I thought was to upgrade the bow arrows with the piercing upgrade from the chubby cat and shoot a shielded robot guarding a door, but in order to upgrade it I need dark steel and I have no idea where to get it. Probably not a great plan anyway, feels too stretched)