Approximating the set of witnesses of a BPP algorithm
The idea suggested to you was helpful.  It basically amounts to suggesting a candidate algorithm $\mathcal{A}'$.

Your next step is to try bounding $|W(\mathcal{A}',x)|$  and $|\{0,1\}^n - W(\mathcal{A}',x)|$ for that choice of $\mathcal{A}'$.  See what you can come up with.  See if you can relate $|W(\mathcal{A}',x)|$ to $|W(\mathcal{A},x)|$ etc.