Step 1: Analyzing the reaction.
The given reaction involves the reduction of a nitro group (NO$_2$) to form an amine group (NO$_2$ to NH$_2$) and an alkene group (CH=CH) undergoing hydration. This is a typical reaction for the reduction of nitro compounds and hydration of alkenes. The reagent H$_3$O$^+$ (aqueous acid) facilitates both processes: it reduces the nitro group and promotes hydration.
Step 2: Analyzing the options.
(A) K$_2$Cr$_2$O$_7$: Potassium dichromate is an oxidizing agent, not a reducing agent, so it is not involved in this reaction.
(B) KMnO$_4$: Potassium permanganate is an oxidizing agent, so it is not suitable for this reduction reaction.
(C) H$_3$O$^+$: This is the correct answer. Aqueous acid is commonly used to reduce nitro groups to amines and to hydrate alkenes.
(D) LiAlH$_4$: Lithium aluminium hydride is a strong reducing agent, but it would not be used here for hydration.
Step 3: Conclusion.
The correct answer is (C) H$_3$O$^+$.