Glory in the slaughter of your enemies using the Eyelander.
It's time for a taunt kill achievement! Every class has an achievement like this (well, except the Medic) and the Demoman is no different. You must have the Eyelander to pull off this achievement, naturally. To do this in normal play, sneak up to an unsuspecting Sniper (easiest by sticky jumping onto the balcony in 2fort) and taunt next to him. It'll take a few seconds, but you'll get the achievement if you manage to cut off his head. The taunt is slow, but not as slow as some others, such as the Scout's batter taunt. To farm this achievement, just have a buddy stand still while you kill him.
Note: Decapitating enemies using the Eyelander taunt counts towards your heads total, which means that you gain health and speed from it. It also counts if you decapitate a friendly player through friendly fire. The name is a possible reference to scotch tape, which is the most common form of adhesive tape.
The Targe Charge
Charge and kill someone with your shield bash.
This achievement is exceedingly difficult thanks to the low amount of damage that the Chargin' Targe does. In a full charge, the Chargin' Targe will deal approximately 25 damage to whatever it hits. In other words, the target has to be almost dead in the first place in order to do anything. The easiest place to do a full charge is on the bridge in TF2, so it's best if you do it there. Beyond that, it's pretty much luck.
To farm this, have a friend play a Soldier. Have your friend rocket jump himself down to 25 health or below. Charge into him with the Chargin' Targe. Congratulations, you now have the achievement. Possibly useful is farmed alongside the Ain't Got Time to Bleed achievement for the Soldier. One of the easiest achievements to farm, so it is suggested that you farm it.
Note: The critical swing of the Eyelander during a charge does not count towards this achievement. That is for the achievement below (Beat Me Up, Scotty).
Beat Me Up, Scotty
Use a full charge critical swing with the Eyelander to kill 5 enemy players.
Finally, an achievement to combine the flavors or the Chargin' Targe and the Eyelander! As you most likely know, the Chargin' Targe charge allows the user to perform a normally impossible critical with the Eyelander. The critical strenght is determined by the length of the charge, with a medium-length charge delivering mini-crits and a full-length charge delivering full criticals. Simply pull off long charges and kill players with the subsequent critical to get progress towards this achievement. Chances are you will get it through normal play just fine.
To get this in farming, get a friend to join you on an empty 2fort server. Charge across the bridge at your friend on the other side, and then chop off his head. Do this five times for the achievement. It's as easy as that. 2fort is recommended purely because the bridge provides a good, long, clear avenue of attack.
Note: An obvious reference to the famous "Beam me up, Scotty," line present in the Star Trek: The Original Series.
Something Stickied This Way Comes
Kill 30 players with air burst sticky bombs.
This achievement is easy or hard, depending on your understand of the Demoman class. If you are a skilled Demoman, chances are you already have this achievement. In order to get it, you must use your sticky bombs as an offensive weapon. Shoot them into the air and detonate them above the heads of enemy players to deal damage and kill them. This is a common tactic in competitive TF2, so it's not exactly an unknown. You can weaken players with your Grenade Launcher before you get the kill. The sticky bomb just has to be in the air when you detonate it for the kill.
To farm this achievement, just get someone willing to die over and over to airbursts. Do it 30 times and you get the achievement. It's sort of a grinding achievement, although the amount of kills (30) doesn't mean it is as tedious as some other grinding achievements. If you play a Demoman for a night or two and airburst effectively, you'll have this achievement in no time.
Note: The name is a reference to the phrase "By the pricking of my thumbs, something wicked this way comes." It's a line in the play Macbeth (surprise) spoken by the three witches near the very beginning. The something wicked is Macbeth himself. The line was later used as the title of a book by Ray Bradbury and a movie based on the book.
The High Road
Sticky jump onto a cap point and capture it.
This achievement is extremely easy. When you are running towards a capture point, simply lay a sticky bomb at your feet and detonate it so that you land on the capture point. Stay there until it is captures. Voila, you have the achievement. You can afford to barely miss the control point, as long as you stand on it within a second or two. This is one of the first achievements you will get, most likely.
To farm this achievement, simply find an empty control point server or start your own. Play on either team, wait for the round to start, and go sticky jump onto the control point to capture it. While it won't count within the server's logs as a real capture (since it took place without any palyers on the opposing side), it counts for the purposes of this achievement. Easy the normal way, easy the farming way. It doesn't matter!
Note: Other people can capture the point with you, and other people can begin capturing the point before you jump onto it. Use this to your advantage. If a player blocks your capture, you have to kill them while staying on the point in order to continue getting this achievement. If you do not, you will not get it.