"Typed" here is an adjective. As I think your intent is that "arbitrary" is modifying "typed" and not "data", that is, the data is not arbitrary, but rather the typing of the data is arbitrary, you need an adverb. So you should say "arbitrarily typed data".
No hyphen is needed. You don't use a hyphen when using a conventional adverb-adjective-noun sequence. You only need a hyphen when you have a modifier that is not an adjective. This helps to prevent ambiguity. For example, "a fast moving truck" might mean a truck used for the purpose of moving that travels fast. Or "I found my long-lost ruler": the hyphen makes it clear that the ruler has been lost for a long time, and not that it is a long ruler that was lost. "Arbitrarily typed data" is unambiguous. "Arbitrarily" can only modify "typed" here, because "arbitrarily" is an adverb and an adverb cannot modify a noun directly.