Defeat Baron at palace was a mission in Jak II. Jak overheard a conversation between Baron Praxis and the Metal Head leader, but is almost detected when Daxter sneezes onto the window through which they were spying. Praxis went to investigate, forcing Jak to fight him.
The PlayStation 3 and Vita versions of this mission are related to a trophy named "Don't Let Him Get Away", completing this mission will reward you with a silver trophy.
The Baron will be armed in his Squid mech, a dangerous flying war machine. This mission is a three parter where it gets progressively harder each phase. You can use Dark Jak's Dark Bomb to instantly take out one of his health bars.
First he'll repeatedly fly at a fixed distance away from the balcony, from where he fires a barrage of shots in your direction. The firing line is more or less fixed, so dodge sideways and fire a couple shots at him with the Blaster. When he is out of energy (small bar above his health bar) he'll go to the electrical gate and recharge, another good time to shoot at him. Repeat this until his mech breaks and crashes into the gate; follow him to the next section.
This time he'll send out a swarm of homing missiles. You'll see a targeting reticule on the floor signifying where they'll hit (generally your position) so get out of the way. Take your time to fire a couple more shots at him until he's out of energy again, repeat this until he once again breaks down.
Now is the best time to use Dark Jak. Otherwise you'll have to rely on your Blaster once more. The arena here is bigger but not entirely flat (doesn't really hamper the Baron's mech) but can be a nuisance for your movement. He'll send out fire tornadoes at you that spread out over time, don't try to avoid them within their line of fire since they're too fast. Instead just roll jump and get out of the way. The same goes for his other attack where he attempts to ram you, roll and jump out of the way.
Otherwise there's not much else, whenever you have a spare second use it to shoot at the Baron, as long as you can dodge his attacks and shoot back he'll go down soon enough.