Arduously is the adverb: it tells you how someone does something when that way takes a lot of strength and effort. You worked arduously means you kept going the hard way, with real strain. Though actually, English speakers do not reach for this adverb very often. They are more likely to say worked hard, or to put the weight on a noun: an arduous climb. The -ly form can sound a little stiff, even bookish. You will still meet it in careful writing.