Decapitate your nemesis.
This achievement is easier than you might think in normal play. While you will have died a lot to your nemesis for him to get that status on you, chances are you can still kill him with a classic bellowing charge. That's right, simply equip the Chargin' Targe and rush straight at that nemesis when you have the chance. His head should come off with a clean sweep of your sword, netting you this achievement with little difficulty. The only concern is if your nemesis is a Sniper, as they are tough to charge and decapitate.
To farm this, have a friend kill you a bunch. If they are a Soldier and have the Equalizer, you can get multiple achievements in one go by killing him with a full-blown charge while he has his Equalizer out and he is your nemesis. In fact, you can almost hit a milestone with the amount of achievements you can get in one go like that!
Note: Much like the Eyelander itself, this achievement is a reference to the movie Highlander, which revolved around an immortal Scottish clansman engaging in a fight to the last man with an array of other immortals. It's a classic of the fantasy genre and well-worth watching.
Do 1 million points of total blast damage.
Naturally, you have to have a huge grind achievement that almost nobody except the most dedicated of players will get. The achievement for the Demoman is this, the Tartan Spartan. You must deal 1 million (or 1,000,000) points of splash damage. We don't have to tell you how ridiculous it would be to try and farm this, as you have probably already gathered that it is not something you want to farm. Weapons of the Demoman that deal blast damage are stickies and grenades. This is because the other two weapons are melee only! This blast damage does not have to be to just players or enemies. Pipe jumping or damaging yourself counts, as does damage to Engineer buildings such as sentries and dispensers. We wish you luck with this achievement, as it is going to take a very, very long time to do!
Note: This achievement derives its name from the tartan, which is the most common pattern on Scottish regalia. Many English speakers know the pattern as plaid rather than tartan.
Kill 3 enemies capping or pushing a cart in a single Stickybomb detonation 3 separate times.
This achievement is quite difficult, but this fact is alleviated a little bit by you not having to do it in a single life. To do it, simply plant as many stickies as possible on a friendly point or enemy cart, then detonate them when three or more enemies are over top of them. They should kill the players, getting you progress. The difficulty lies in your enemies destroying or pushing your stickies, rendering you unable to kill three people in a single detonation.
To farm this, get some friends to stand on a point that you have stickies on. Cackle maniacally and blow them to pieces. Do this three times, and you'll get this achievement. On the plus side, if you don't have it already, you'll also get the Pipebagger achievement. There's no other achievements you can really do with this one, besides the grinding ones such as Tartan Spartan.
Note: While a reference to the Demoman's nationality and the guarding of points, this achievement is also a reference to a commercial product. Called Scotchguard, it is one of the most useful stain removers on sale.
Kill 200 players defending a capture point or cart.
You are going to grind more doing these achievements than a blacksmith sharpening an ancient rusty sword. Here's another one! This achievement is worded funnily. It doesn't mean for you to kill players that are defending a point, but rather you must kill players to get a defense credit. This is easiest when they are capturing a point that has your stickies on it, so if you are playing defensively in most of your games, chances are you will get this achievement relatively early on. If you are playing offensively, you will have a great deal more difficulty with this achievement, as you won't have much opportunity to get credits towards it. Regardless, play a lot and you'll get the achievement.
Note: This achievement is a reference to the movie Braveheart, which was a fictionalization of the Scottish rebellion led by William Wallace against King Edward I's rule of both Scotland and England.
Cry Some Moor!
Destroy 50 buildings.
Grinding is the name of the game with this set of achievements, it seems. Perhaps it's appropriate, given that these are the last achievements in the list. To get this achievement, simply get 50 building destructions. It's a very easy achievement to get, and farming it is actually fairly simple as well. If you get an engineer or two to continually build in front of you, you can rack up the 50 destructions necessary in no time. Buildings do not have to be finished, so an Engineer can simply stand next to a bunch of ammo and continue rebuilding his destroyed buildings.
Note: This achievement title is an in-house reference (for once) to the Demoman taunt of "Cry some more!" said in a heavy Scottish accent.