Aranea will drop you off back at Lestallum and although she would love to come with you, she is only doing what she is paid to do. Seems like helping a king reclaim his throne could be quite lucrative, but she apparently isn't keen on extending a line of credit that puts her ass on the line and gambles on your success. It also seems there's some sort of trouble at the power plant, daemons messing around with things, unstable generators... you know, the exact sort of thing the heir to the throne of Lucis shouldn't be put at risk dealing with. Fortunately for Lestallum, Noctis needs help refining that Mythril ore, so a favor for a favor it is.
Run north-west across the bridge to the reactor, then circle around the outside clockwise to meet up with the other hunter assigned to this task. Hmm, that voice sounds vaguely familiar... Oh well, head inside the plant and right before some stairs leading to a metal bridge you'll find a loot spot ( Silver Bangle ). Continue north-east across the bridge to find the daemons - some Goblins and a Garchimacera. The former are easy prey, but the latter is a little bit sturdier, being a level twenty-four beastie that's weak to swords, shields and fire, while strong against lightning.
Unfortunately, something goes awry and you're told to get the heck out of there. The other hunter doesn't want to leave unfinished business, so you will have around five minutes or so to clear out all of the daemons, which is more than enough time. Just circle around the central area to keep finding new enemies to kill until you've gotten rid of them all, earning you 5 AP in the process for completing the bonus objective.
|For clearing out the daemons in the power plant||EXP 500 / Mythril Component|
Leave the reactor and Gladiolus will officially rejoin the party, after which Iris will show up and - after completing ignoring her brother's wounds - say she'll deliver the Mythril to Cid back at Cape Caem. When you're ready to continue the story, that is where you will need to go, which is only a fast travel away now.
However, it should be noted that some new side quests have opened up in Lestallum, one of which is from Holly, the woman whom you helped by going into the power plant. Another one will be received automatically as you head past the Noodle Wagon, presumably en route to the Regalia parked outside of Lestallum. More importantly, The Vesperpool is now open to you, meaning it's time to explore that area more thoroughly. Also, since you're a bit stronger now than you were before, it's time to turn your attention to some dungeons and side quests that have, until now, gone ignored. namely in and around The Vesperpool, Ravatogh and Malmalam Thicket.