Correct spelling, explanation: base adjective for this word is actual. To create an adverb from an adjective we add the suffix -ly. Since actual already ends with consonant l we need to double it. Therefore the correct spelling is actually, not actualy.

Definition of actually:
adverb, as an actual fact
The teachers I liked in high school were actually the most strict.
I was actually very impressed by his sense of humor and wittiness.

Incorrect spelling, explanation: in this word l should be doubled, because the adverbial suffix -ly is here added to the word actual, already ending with l. Thus actualy is an incorrect form and the correct one is actually (actual + -ly).

Incorrect spelling