As you’re probably aware of (and was covered earlier in the guide), Tempered monsters fall into on of three categories - Threat Levels - depending on the type of monster. Generally, monsters you encountered earlier in the game are lower Threat Level monsters, while everything you encountered during or after the First Wyverian Ritual during the main story count as Threat Level Two monsters. All Elder Dragons are Threat Level Three. Not all monsters have Tempered versions:

There are a few optional quests and assignments where you’ll find Tempered monsters, but most of them can be found in investigations. As usual, to unlock these investigations you’ll have to go on expeditions and find the tracks of these Tempered monsters (which are easily spotted thanks to the special blue Scoutflies that highlight them). This can be a time-consuming endeavor, but you can speed the task up considerably by crafting the Hunter’s Headgear α, which will give you the Scholar skill and the Scoutfly Range Up skill.