Arrow’s Impossibility Theorem, as I understand it, applies quite broadly to voting systems. To put it simply, you can’t avoid it. You just decide what trade offs you want to live with.
Looking at it closely I think it gets particularly gruesome when you try to do a "perfect" job of determining people's preferences.
Arrow's theorem applies only to ordinal voting methods. Approval is not actually subject to Arrow's theorem; it's not even well-defined whether it passes the criteria.
However, there are various voting impossibility theorems inspired by Arrow which do apply to approval. Most notably, Gibbard-Satterthwaite.