いきなり

いきなり means "suddenly", "without warning": something happens, or someone does something, with nothing leading up to it. It is an adverb and goes before the verb or at the start of the sentence.

Skipping the first steps

いきなり also means starting at the end without the steps that normally come first: straight into the main topic, straight into the advanced class, perfect on the first try.

いきなり or 突然

とつぜん突然 is about surprise: an event nobody expected. いきなり is about the missing lead-up, and is most at home with what a person does. For a sudden event, both work.

For skipping steps, only いきなり carries the meaning. 突然上級コースに入った says only that it was unexpected; いきなり adds that the beginner classes were skipped.

突然 is also the more formal of the two, at home in the news, and it works as a noun: とつぜん突然のあめ雨, "a sudden shower". いきなり is conversational.

Usage notes

These go beyond describing something sudden.

Complaints with ないで

Asking someone not to spring something on you is いきなり with ないで.

いきなりですが

As an opener, いきなりですが apologises for raising something with no warning, like "sorry to spring this on you".