Although to tidy up is one acceptable translation of sprzątać in another exercise, Duo currently rejects to tidy up in this one (an incubator omission?), though it should clearly be accepted here too.
I first learned sprzątać = to tidy up from a Polish native speaker, and my Polnisch - Deutsch Taschenwörterbuch (1981) doesn't even mention the alternative meaning to clean.
So, why isn't "I'm trying to clean this place" accepted? It does kinda have a different meaning - that it is cleaning the whole space, and not just some part of "here" - but still I believe it's a suitable translation.
For the sake of the question, though, how would I strongly indicate in Polish that I'm actually cleaning "this place" completely and not just scrubbing away in the corner.