You can just jump around the first lava fall into the water without taking damage. Then just swim through the next 2. You'll need to drop out of the 3rd into the fire to get around the 2nd lava fall. If done quickly you only take 1 heart of damage before getting into the next water fall. While in the water, make sure you take the time to fully regen before attempting to get through the last lava fall. There's no getting around this one, you have to swim through the lava, and it'll almost kill you even if done perfectly. If you manage to get through, just swim up the water & drop onto the platform.
The next part is harder than it looks. This ladder jump isn't that hard, but a lot of people fall here. You don't need to sprint jump, you just need to make sure you don't hit the side of the ladder. Once you climb up the first, you have to make a 2nd ladder jump. Again you don't have to sprint, and after you make the jump just head into the tunnel.
This next part was designed by fellow Scottlander wolfsorrow. It looks impossible, but there's water just beneath the lava. So jump into the lava, and sink below the top layer. Don't try to jump far, just up so you gain some downward momentum when you hit the lava. Once through, you'll need to carefully swim without hitting the lava above AND below you.