Dead set, meaning (1) fixed on a purpose or (2) resolutely, is two words. Set in this phrase is an adjective meaning fixed and rigid, and it is modified by the adverb dead, here meaning absolutely. Dead set is often a phrasal adjective, but it usually follows what it modifies, so it doesn’t need to be hyphenated. When it precedes what it modifies, however, dead-set is correct.
The one-word deadset has not fully caught on as a replacement of the two-word form, but it is gaining ground may someday gain acceptance.
Examples
Dead-set is often hyphenated—for example:
[B]ut the chubby crook is dead-set on getting the bike and keeps going back to try and chop the tree down. [The Sun]
Butler seems dead-set on having listeners focus on the music rather than the persona behind it. [NPR]
The main justification for the hyphenation is that it prevents readers from misinterpreting the word dead. This is understandable, but there’s no grammatical basis for the hyphen, and any misinterpretation is fleeting if it happens at all.
Most publications take the more grammatically conventional route, omitting the hyphen—for example:
Owners are dead set on ending the oversight of the Minnesota court system. [Forbes]
[M]any environmentalists and social justice groups are dead set against costly technical schemes to manipulate global temperatures and the atmosphere. [Globe and Mail]
[B]oth say they are dead set against any tax increases. [New York Times]