To disillusion someone is to rid her of an illusion, like lifting up the curtain to show that the wizard is just a man. Dissolution, on the other hand, is when everything falls apart. Both are disappointing.

The verb disillusion needs an object, as in you have to disillusion someone. Toto accidently disillusions Dorothy of her belief in the magical wizard. (The word is more common as an adjective, as in poor disillusioned Dorothy.) It's also a noun, when it's a feeling of disillusion, a loss of enchantment. Here are two examples:

He has raised expectations so high that whatever he does as PM is bound to disillusion some.  (Ottawa Sun)

My disillusion was growing and I was relieved when they laid me off with a generous severance. (New Internationalist Magazine)

Dissolution, always a noun, is like disintegration. There could be the dissolution of a marriage, band, political party — and if you're Edgar Allan Poe — human body. In "Masque of the Red Death," Poe describes the symptoms of the Red Death: "There were sharp pains, and sudden dizziness, and then profuse bleeding at the pores, with dissolution." Yikes. Most examples of dissolution aren't as exciting:

The singer's wife had filed for dissolution of marriage in September last year, according to San Diego Superior Court documents. (BBC)

Until its dissolution in January 1994, the Christian Democratic Party dominated, furnishing all but three postwar prime ministers. (New York Times)

Although the words sound alike, the difference is after the "dis" (meaning "not"): disillusion is not an illusion, and dissolution is not a solid solution, it breaks up like paper in water.