Working on P.D. Magnus. forallX: an Introduction to Formal Logic (pp. 182, exercise B. 9):
$ \def\fitch#1#2{\quad\begin{array}{|l}#1\\\hline#2\end{array}} \fitch{\neg (W \to W)\\(W \leftrightarrow W) \wedge W\\E \vee (W \to \neg (E \wedge W))}{ \fitch{W}{ W }\\ W \to W\\ \bot } $
As I understand, I need to derive a contradiction assuming those sentences as premises. Is this the right approach?
Yes. That is sufficient.
You can also argue that the first premise is by itself a contradiction (because it cannot be satisfied by any interpretation of $W$), so therefore all three premises do form a jointly inconsistent set (since there is no interpretation of $\{E,W\}$ that will simultaneously satisfy all of them).