How can I dissolve nickel(II) oxide?
As mentioned by @Mockingbird, nickel oxide is somewhat soluble in potassium cyanide which will dissolve the oxide to form nickel cyanide, $\ce{Ni(CN)2}$ and potassium tetracyanonickelate, $\ce{K2Ni(CN)4}$  but potassium cyanide is very, very toxic.

Do not use it until and unless you are a professional chemist.