Had some nice runs just now. Rolled into a group at pursuit level 4 and managed to break the horns. Then we started at 1, went to 3 and finally 6, all with the same group. Everyone knew what they were doing, there were no quest fails and we managed to break the horn plating every time.
Got a nice IG out of it. R7, but actually better than the normal R8 Kirin IG. Thunder damage is lower (300 against Kirin's 360), but raw damage is 100 higher, it has +20 defense and the Kinsect boost is speed instead of element. Plus it has the Tzitzi-Ya-Ku design which I think is pretty great. I welcome the chance to wield weapons with desgins from less impressive monsters like Tzitzi over the usual Vaals and Nergigantes.
Defeated the main story today, Hunter Ranked unlocks all the way to 29, opening up the Dual Tempered Bezel.
Defeat it first try (The Bazels fought eachother, I just did some clean-up afterwards) and HR ranks up to 42 on success.
Now to hunt for gold for Kulve, what level of Kulve investigation do I want before I start joining sieges? And do I go with my Royal Burst or my Nergal Reaper? (Still need a few more materials for Catastrophe's Light.)
Level of investigation doesn't really matter. You need at least one track to initiate the quest, after that it's all good.
As for pursuit levels: you are set back to level 1 after you successfully complete a siege. So if you jump in at level 1 or at level 6 (the max) it doesn't make much of a difference in the long run. In fact, starting at level 1 might be preferable because you get more shiny drops to pick up and another chance at breaking its horn plating, which grants you an additional three carves (and a chance at gems if the RNG deems you worthy of its blessings).