I haven’t really found a complete breakdown of Tempered Investigations and the best way to go about handling their acquirement, and it took me a bit of trial and error to really figure out the best method for going about it. Even now, I have friends as high / higher HR rank than me that still act shocked when they see me with Tempered Elder Dragon Investigations, and always ask “Wait, how did you get that!” when I invite them to the group.
It’s not very difficult, but the in-game prompts can be misleading. I’m going to quickly share all of the tips I’m using to farm these, and if you already know all of this… great! Hope you’re having as much success as I am! If you are not, well… here you go!
First, Tempered Investigations are broken in to three categories. There are easy (one flame), medium (two flames) and hard (three flames) Tempered Invests. The HR check on these is HR13 for easy, HR30 for medium, and HR50 for hard. As far as I know, you will not start unlocking these until you hit those respective levels, but I could be wrong.
Unlocking a Tempered Investigation is tied purely to the difficulty of the flame, not the mark itself. What I mean by that is, finding Anja footprints doesn’t mean you’re going to get an Anja Investigation. It means you’re just going to unlock an Investigation at the easy tier difficulty – it could be for any dino in that category.
ONLY Footprints and Trailings unlock Tempered Investigations. Unfortunately, while fighting a mark, any Invests you see pop as a result of breaking pieces or killing them will unlock only regular, non-Tempered Investigations. For some reason, they don’t recognize the Tempered beast itself as being Tempered, only the Footsteps.
Contrary to the Tutorial Tip, you do not have to be in an Expedition to unlock these. You can, in fact, continue to unlock them in Tempered Investigations themselves, so long as you carefully and patiently follow your Tempered mark around picking up their Footstep trails. It seems like pure RNG, and I go on hot and cold streaks, but it 100% works. I’ve even spent a full 50 minute mission once solely walking around grabbing the Footsteps, purely to unlock a broad category of further missions!
The Decoration rewards are directly tied to the difficulty of the Investigation. Pretty self explanatory, but for full transparency… easy usually gives Rank 4 Appraisals, sometimes Rank 5. Medium usually gives Rank 5 and 6, but sometimes Rank 7. And Hard usually gives Rank 6 and 7, but sometimes Rank 8. Rank 8 Appraisal items are not actually decorations, but rather the exclusive Augmentation materials you need to upgrade your weapons. There are Rank 7 versions of these as well, that can drop from both medium and hard.
When looking for your first initial Tempered Investigations, map out an Expedition’s Footprints. They are NOT random, they are fixed locations that will consistently spawn in the exact same spot. The randomness is in which beasts you get, but those beats will always have their Tempered Footprint in an Expedition in the exact same spot every time. I found Pukei Pukei saliva at the butterfly hill in Ancient Forest consistently, and for farming medium/hard I’d rotate between Rotten Vale and Elder’s Recess. In Rotten Vale, there’s typically a pile of Decayed Flesh at the big pile of bones where you encounter Vaal Hazak, and Odogaron Footprints near his hiding place. In Elder’s Recess, there can be Nergigante Spikes in the big wide opening just before the zone in which he typically spawns in, a Lava Fish Footprint in the Southwestern-most lava area, and 100% of the time I found a pile of Kushala Feathers right at the peak where it sleeps when wounded. By farming these spots consistently, I unlocked my initial medium/hard Tempered Investigations, and from that point on I continued to open up new Invests by following the beasts around in those Investigations, picking up their footprints, so on and so forth.
Again, if this is all obvious information, then sorry for wasting your time! I’m just sharing a very direct and to the point set of tips to help you out as I couldn’t immediately find this myself when I was originally looking, and as said I get asked about this a lot. So there you go!
EDIT: I realize now you could probably follow around the Tempered Kirin or the Tempered Hazak in their respective Blacksmith missions. This would work just the same as following them around in an Investigation, and would probably be quicker. Just remember, don’t engage them – simply walk around looting their trails!