Well, looking back on my explanation, it's overly simplified. I'll elaborate:
Verkligen emphasizes the reality of what's stated. "Filmen är verkligen bra" means that "The movie was really good" in the sense that the reality of the quality of the movie is what's being emphasised.
Egentligen points out that something isn't what one might expect. "Jag är egentligen rörmokare" means that "I am actually a plumber" in the sense that one might not have though that.
Does that perhaps help a little bit?