"I have really tried."
Translation:Jag har verkligen försökt.
Well. Verkligen here means that you've really tried, as in that you've made quite an effort. Riktigt on the other hand, cannot be used in this context as it has to do with reality and/or truth. You could say "jag har försökt på riktigt" to mean that in actual reality, you have tried, as opposed to pretending to do so.
Does that clear it up a bit?
This is a tricky one,
Verkligen is used to emphasize that something "really" is in a certain way.
"He is really kind" - Han är verkligen snäll
"She is really tall" - Hon är verkligen lång
Egentligen is used to point out that something, contrary to what one might believe, is in a certain way.
"The dog is really quite kind friendly" - Hunden är egentligen ganska snäll
"Many people think that Columbus discovered America, but it was really the Vikings who did it first" - Många tror att Columbus upptäckte Amerika, men det var egentligen vikingarna som gjorde det först
In the first sentence, "the dog" has obviously been hostile or shown a bad behaviour, but the person saying this wants to point out that this isn't showing the dogs true nature, so contrary to what you believe right now, the dog is actually quite friendly. If you'd replace egentligen with verkligen, the sentence would change to mean that the dog is showing a good behaviour and this really shows.
In the second sentence, egentligen could be replaced by faktiskt, which means "as a matter of fact". However, verkligen would not work.