When you're speaking quicker or feel like being a little lazy, it's pronounced like "ak-sh-ly," but if you're emphasizing the word, it might sound like "ak-ch-ly." But since I'm a lazy speaker, I almost always pronounce is with a "SH."
Here are some sentences someone might say differently:
There's actually a lake near my house. (Ak-sh-ly)
Actually... I don't have any left. (Ak-ch-ly)
Some people use both in either situation.