“I can definitely tell you're getting better.”

Your friend is learning to play the guitar. He's frustrated because he doesn't think he's improving. But you do think he's improving. You say:

I can definitely tell you're getting better.

(someone) can tell (clause)

When you "can tell" something, it means that you know it by experiencing it:

I can tell that you're lying to me.

Could you tell I wanted to leave?

You can leave "that" out in casual conversation, but in formal speaking or in writing you should definitely include it:

I can definitely tell that you're improving.

definitely (do something)

When you use "definitely", it means that you're sure.

"Definitely" is often used together with "can tell":

I can definitely tell that you've lost some weight.

(be) getting better

When you're "getting better", it means you're improving. "Get better" is a more casual version of "improve".

"Get better" also means to recover after a sickness or injury, by the way.