Master of the Wilds can be a huge pain to finish, simply because some of the creatures you need to find can be a little elusive. Several of them can be found during missions, however, making these hard to find creatures much easier.
1) Kill 3 Spiders
These little things appear all over Mordor, though frequently near caves. Use your Wraith view to spot them easier. You can kill them in almost any fashion you can think of, including just stepping on them. Kill three however you like.
2) Kill 5 flying creatures
Much like the spiders, you'll find these all over. You can find bats frequently around caves and some other creatures frequently perching near strongholds. You'll have to shoot these out of the sky, so make sure that you have Focus when hunting them. Also keep in mind that when your aiming at them, your reticle will shrink a smidge as it goes over your target, indicating that you've lined up the shot.
3) Kill 3 Caragors
Early on, this might be a little bit tough. Caragors are all over the place, including in cages and roaming the wild. Later in the game, you'll acquire an ability that allows you to mount one instantly. At the point, you can simply kill it while mounted by holding R2 and hitting Circle (I believe).
However, because some of the later hunts are a little tougher to find, you'll want to kill these earlier. Just find Caragors near some Orcs and use the Orcs to help you kill it. Do this three times.
4) Kill 4 Rats
You'll tend to find these around strongholds and large camps. They'll scurry about low to the ground. They aren't generally difficult to find, but the proximity to Orcs means you usually have other things on your mind. Just stay hidden and keep your eyes peeled. You'll find them eventually
5) Kill 8 Ghuls
While not plentiful in most of the open areas of the world, they come out in droves in some areas. If you find one, remember where it is so you can return later in the game for this.
If you don't find any places, there's a pretty good one by the Forge Tower
6) Kill 3 Bats
You'll find bats by/in caves. Check out the caves and you'll eventually find some. Much as the previous "flying creatures" challenge, make sure you have Focus when you go hunting.
The two points I've had the most success with were in the Sea of Nurnen area (the second area). On the far right side, just north of the eastern Forge Tower in (Harad Basin) is a cave nestled in the cliffs from which you can zipline down. I've found some near the mouth of this cave.
There's also a cave on the far western side of the area that is useful. From the western most Forge Tower (Tirith Mesas), go north to the cave in Celon Poros. You should find a cave with a large horned Graug in it (you'll come back for him later). Sometimes you can find a huge swarm of them by the mouth of the cave.
7) Kill a Graug
You can kill any Graug for this. The aforementioned cave in the previous challenge works. You can also sometimes fine them spawning near Forge Towers, so you can hop from one to another to find them. I've had luck with the northwestern most Tower in the Sea of Nurnen (Cape of Nurn)
This can also be done by partaking in the main story. There will be a set of missions involving a dwarf named Torvin. During one of the missions, you'll take down a Graug.
8) Kill a Dire Caragor
The easiest way to do this is the final story mission with Torvin. After you kill your first Graug with Torvin, you'll set off to kill a horned Graug. After this mission is complete, you'll find yourself already riding a Dire Caragor.
If that option isn't available, head to the Sea of Nurnen after it becomes available through the story. Find a Caragor and just ride around the area until you come across a Caragor with a health bar. More than likely, you'll see the health bar before you ever see the Caragor. Once you find it, kill it however you like.
9) Kill a Ghul Matron
This is regarded by some to be the toughest to find. It really isn't. By the southern most Forge Tower in the Udun (Udun Crossing) is a great place to get this. There's a small pass SE of the tower. Jump down and start going through the pass (at night) to be attacked by Ghuls. Kill one or two, but leave some alive. Eventually, they'll begin to run away while showing the "about to sound the alarm" flash above their heads.
When this happens, let them go. They'll run away, dig into the ground. It might seem like something went wrong but after a few moments of quiet, more Ghuls will come. Kill them slowly so that each group might send more Ghuls to raise more alarms. Keep killing and letting Ghuls go until eventually a Matron appears.
When the Matron appears, kill her. She's a pretty able fighter so you might want to just shoot her with charge shots. Otherwise you have to jump over her, hit her twice, and jump over her again.
10) Kill a Horned Graug
You may be able to find these wandering around in the Sea of Nurnen, but you can also find one frequently in the cave in the in Celon Poros. There's not much in the cave. If you don't find it, leave, advance time, fast travel back to Udun, maybe run some side missions, then return.
Otherwise, grab a Caragor and ride around the Sea of Nurnen until you find one.
That should help you get all 10. Unfortuntely, some of these are very dependent on a measure of luck, and there isn't any way to over come that. If you keep an eye out while doing other things, however, you can cut down the amount of time needed for this considerably.