Part 4 - I have to go up now?

This really doesn't make much sense, we spent a lot of time going down, now we have to go back up. Makes you wonder if there's a secret bridge from Part 1 to the end boss...

Or the architects were drunk, which guessing by the decor, probably is more likely.

Loadout

You want a least one distance weapon here, you can keep most of the Taken at bay. There are a couple of points where you'll have to go toe to toe with a Taken Knight with a solar shield. So an Avalanche in the Power slot is quite useful.

The first 4 Wizards are also solar shielded. And if you take them all on at once they'll wipe you out quickly. So approach with cover, take one out, wait for one to rush you, then you can take the other two out easily.

There isn't much more to it except the next checkpoint is the end boss, so be careful with your jumps and on the boop wall.

Time to end this. Part 5 - End of the road