Xenoblade Chronicles X features giant mechs called Skells. However, you're going to need to put in a big chunk of playtime if you plan on acquiring one of these puppies. I've personally clocked in 29 hours until I got my Skell License quest, so don't go thinking these bad boys become available shortly after you start playing.
After you complete Chapter 6, you'll get a prompt from one of the main NPCs that you're now eligible to go get your Skell License, which is what you need in order to pilot Skells. Acquiring your license isn't a simple task though, it's actually 8 tasks.
The license exam is split up into 8 individual missions that correspond with the 8 different divisions in the game. You'll need to complete a mission that's specifically catered to that division. This is also a cool way to see what each division specializes in, aside from just reading about it, and give you an idea if you want to change divisions based on this.
Proficiency Exam 1: Pathfinders
For this one, you'll simply need to plant a data probe at site 117 in Primordia. Chances are that you've already planted this data probe, as it's not far from New LA. However, if for some reason you're still missing this one, check out the image below to find it easily.
Proficiency Exam 2: Interceptors
For this one you'll need to head to Noctilum to defeat 12 Blitz Blattas. Luckily, the map points you in the right direction so you'll simply need to teleport to a nearby data probe. There are two spots where these spawn and both will be marked on your map. Don't worry, these are small bugs that shouldn't be giving you any trouble at this point in the game.
Proficiency Exam 3: Harriers
For this one you'll need to defeat a Tyrant, which are named versions of normal enemies. The Tyrant in question is Shatskikh, the Flash, who can be found North of New LA in an area called Northpointe Cove. Don't worry, the mini-map will point you in the right direction. The mission states that it's a rare spawn though, so if you don't see it, just simply keep fast traveling to Northpointe Cove since by now you'll have the location discovered. I fought him at night, so if you're having trouble spotting him, try changing the time to night at one of the time changing locations, and then come back to this spot.
Proficiency Exam 4: Reclaimers
This is one of the easier tasks, as you simply have to find a relic in Noctilum. The relic is also pinpointed on your map and mini-map, so simply follow the yellow arrow to get to it.
Proficiency Exam 5: Curators
The Curators exam is probably one of the more annoying, especially if you haven't focused a lot on picking up a lot of the blue crystals as you explore each map. You'll need to collect a specific item in each of the first three starting continents, Primordia, Noctilum and Oblivia.
Chances are, if you've explored a lot of Noctilum and Primordia, you'll already have the necessary items for those two locations; being 8 Rock Armadillos and 6 Multi-speckled Ladybugs respectivelly. If you haven't gotten either other those, you can find Rock Armadillos by FN Site 216 in Noctilum, which is in the second, larger part of Noctilum in the South. Multi-speckled Ladybugs just North of New LA at FN Site 112.
This is the general area where you'll find Rock Armadillos in Noctilum
This is the general area where you'll find Multi-speckled Ladybugs in Primordia
The Beagflea Squashes can be tricky to find, only because you most likely haven't been to the location where you can find them. You'll need to make your way to the North-East of Oblivia to Lake Basel. Once you're there, this item can be found all around the lake, and even floating on top.
Lake Basel is located all the way North-East. That's where you'll find Beagflea Squashes​
Proficiency Exam 6: Prospectors
Easily one of the more difficult tasks, if you don't particularly have a lot of Research Probes. However, by now, you should have at least a Duplicator Probe and a Booster Probe, both of which were essential for me to hit just over 15,000 credits in one return. What this means is that when you're changing your probes, the bottom number on the screen under Revenue Total must be over 15,000. Here is how I did it.
In my case, I didn't have a lot of Research Probes which boost currency, so I had to get creative with the Booster and Duplicator Probes. The best place I found was in the West part of Primordia, since many of those Data Probe spots are interconnected. As you can see, the top spot is occupied by my Booster Probe (Red), which is then directly connected to the Duplicator Probe (Purple) essentially boosting its effectiveness. Then you want to connect your Research Probes to the Duplicator Probe as it raises their effectiveness exponentially. I don't have it pictured here but you can also connect two more Research Probes to the red Booster Probe above it, which will boost both of their effectiveness as well, though one of them needs to be connected in Noctilum, as it extends outside of Primordia's map screen on the left.
Once you reach get over the 15k revenue on the bottom, simply wait until the game collects it, and this task will be finished.
Proficiency Exam 7: Outfitters
A pretty self-explanatory task. Equip one of the three weapons; Trial Knife, Trial Sword or Trial Assault Rifle, and follow the mini-map to the Giant Grexes and take them out. You only need to kill three with a single weapon, not all three.
Proficiency Exam 8: Mediators
Simply choose one of the three side-quests from the list and complete one of them.
Congratulations!
You just earned yourself a coveted Skell, and completely for free! Not too shabby!