As you move through the Volcano you'll encounter stingers, mantises and metal jackets, which when combined with the small interiors makes the Beam Reflexor an excellent weapon for the majority of this mission. A simple jump, spin kick and fire combo will kill most Metal Heads without any difficulty as you progress through the location.
Soon enough you'll encounter a lone leaper lizard; chase it (watch out for the ground collapsing near gaps) and catch it (use roll jumps and punches to close the distance). After catching it you will have to use it cross a couple of large lava-filled gaps, while avoiding red-hot boulders being blown into the air and blocking your path. Eventually you'll encounter several spiny toad hounds and a ladder up ahead set against a cliff wall.
You will have to dismount from the leaper here, the toads are easily dispatched all at once with the Wave Concussor, and climb up the ladder. Up here you'll have to play as Daxter for a short time, hanging onto a net and avoiding more boulders, lava flowing from the walls as well as three mantises which Daxter can dispatch with one hit. At the end you will see a cutscene, where after you can meet up with Jak again.
From here on you will encounter more metal heads. After a short walk you will see an air vent with a thick, flat, rock next to it. Punch the rock onto the vent and use it to get to the top of the cliff here. Continue on until you get to another Daxter section, where you side down a metal pipe and end up at a section where you'll have to use trampolines to get higher. There are a few toads here, at the top you'll automatically start a cutscene and reunite with Jak. Push this rock onto the air vent too to continue.
A few more metal heads until you encounter three air vents and three rocks at once. Push all of them onto a vent each and the middle will float up, from here on just go higher and higher without any trouble until you reach a lava river. Jump onto the stone platforms here and then jump onto the ladder at the other side of the river, climb up and start a cutscene.
Technically the mission ends here and you're automatically forced to continue with the next one in this line; "Find oracle in Monk Temple".