Appealing to a bad guy's good side might be a losing proposition... but what about offering to help them? If they're bad just because they're lashing out at a world they think hates them, then maybe some well-timed compassion and understanding can create a chink in their armour...

And then you go in for the kill.

Transcript

Luke: Look, clearly you need some sort of medical help.
Palpatine: Have I gone mad? I'm afraid so, but let me tell you something, the best people usually are.
Luke: Let me take you to Polis Massa.
Palpatine: It's no use going back to yesterday, because I was a different person then.
Luke: And who will you be tomorrow?
Palpatine: Who in the world am I? Ah, that's the great puzzle.
Luke: You were a great voice for the people! Before the Empire. You can be again.
Palpatine: I used to be much more... muchier. I've lost my muchness.
Luke: You hold the fate of thousands of worlds in your hands. You have to let me help you.
Palpatine: Why do you think I built a new Peace Moon? It's the only way! They must see that!
R2-D2: Who needs a reason? Building a massive superweapon is its own reward!