It really should be noted that these DO NOT SAVE unless you do something major in the game, or do a manual save. I just lost 2 hours of collecting relics and letters. Literally have to do it all over again because I exited the game without doing so. I even had obtained the achievement for the letters, and now I am missing half. I will still have to get them again probably so I can get the 500XP they gave. This game just lost a few points with me...
Never Saw It Coming
Kill an enemy with a takedown from above
During the Lin Cong I Presume?
mission after collecting the 3 compass pieces, you will have a very easy opportunity for this. You'll get to a point where you must zipline a fairly far distance. At the end of the zipline is an enemy. Just use the zipline and don't shoot him. The achievement will unlock without you even having to try. I would almost call it story related, but if you buy the Line Gunner skill, you could technically shoot him. If you don't buy that skill, you will get this by just playing the game normally.
Freefall more than 100m and live
When you are in the plane and have to freefall out, just don't do anything. This mission is called Three Blind Mice. You are supposed to deploy a wingsuit. Instead, just let yourself fall to the water and get the achievement. This takes literally no effort at all because the game has you fall from the plane at the correct height. All you do..is nothing! When the mission fails, you can continue on and deploy the suit.
Liberate an outpost without triggering an alarm.
Not that this is difficult, but I am a little surprised you didn't mention the animal cages. Plenty of the outposts have animal cages that have wild animals inside. I normally just shoot the front (has the red part on it). If it's a bear or a tiger, often they will kill all the enemies inside. I have obtained at least 3 outposts by shooting/sniping the gate and waiting. One time I was sitting there and a tiger walked by me and ran in and killed everyone for me. I heard screaming, explosions, and eventually everything was dead including the tiger.
Memory to Spare 20
Gather all the memory cards.
A simple snapshot of what the laptop looks like would probably be fine. The video on all 20 is way overkill, especially when you have to liberate all posts anyways and they unlock fast travel to the laptop areas.
Heartless Pyro 10
Kill 50 enemies with the flamethrower (Single Player only).
If you get 10 kills and then die without the game saving, then you will lose those 10 kills. I actually have 38 kills but I have obtained the achievement. Stats do not save like relics or letters. You must get them again (all your ammo comes back when you die).
Kill a target from 70m or more with the bow (Single Player only).
Okay, good point in the marking the camp and so forth, but you put explosive arrows as a side not when it should be your main method. I must have shot 50+ arrows at people. I decided to try my luck with explosives and got it in 1 attempt. This is because the arrow seems to be more accurate when shot and aiming. If you are higher elevation than the enemy, it works extremely well. Even if you miss. Another little note, the achievement pops instantly. In the video on the PS3 version, there seems to be a big lag.
Getting Even 20
Complete "Payback" Co-op map (Online/Offline).
For the Co-op map ones, you could say "see Getting Even achievement description". Then you can kind of explain what it is all about. Are they short missions? Is it easy to just leave your 2nd controller on while you play? Is there a set difficulty or can you choose? Do your skills carry over from single player?
Fully Inked 30
Earn every tattoo by learning all the skills.
You claimed you would list the important ones but never did. You mentioned about ones that need certain types of kills but left the details out. Basically the skills unlock in three different ways. By progressing through the story, by buying a skill next to it that is unlocked, and by completing certain things the game demands (buy 3 armor, kill 10 with pistol, etc). If you die, the stats will go back to what you had before death unless you have hit some kind of save or check point.
Island Liberator 40
Liberate all outposts.
You can mention about letting the animals loose. You can go into more detail about how to disable the alarms (you can shoot/snipe them from distance with silenced weapon). You can mention silenced weapons are your best friend here. You can also say what happens if an alarm sounds. A ton of enemies rush in and you must also kill all of them. So the 3 to 5 guys can actually turn into 15+ very quickly.
Say Hi to the Internet
Find the lost Hollywood star
You had a lot of videos for other stuff like memory cards (which didn't need a video) but surprised to see possibly the one thing that would help a little more just to kind of "see" what it looked like, is this one. I am providing images of what this all looks like.