As soon as the mission starts, swing to the next building and watch the scene. Once the automatic devil trigger has been activated use angel lift on the targets to reach Mundus' eye then pull it.
Once inside the building, continue forth and pull the debris out of the way. Destroy the obstacles until you reach an office. After the scene, use angel lift to get out of the way and head to the next building rooftop. From hereon, you'll need to damage his arms. His attacks should be easy to evade. Just be mindful of the shockwaves that will be released upon impact. Use double-jumps, aerial evasion and angel boosts to avoid these shockwaves. Close the distance quickly using angel lift as well. Keep concentrating on whatever arm is available; his left arm will be destroyed first however. Once he starts spewing lava on the roof, find the nearby angel lift target to swing to the next building.
Keep repeating the process until you take out both his arms. Once done, he'll start firing three energy orbs at consecutively. Evade them then pull yourself towards his mouth once he gets near. Keep damaging him until his last hp bar is depleted. Mission complete.