Get 3 dominations in a single life.
This achievement will require a little preparation before you can pull it off successfully. Specifically, you will need to kill three players twice each without dying to them or anyone assisted by them. It's tough to do, but it's necessary if you want to get this fairly difficult achievement. The alternative is to just be an absolutely awesome Soldier. Once you've done the prep work, kill your three targets in a single life and you'll ge the achievement. This is easiest on any map with defined offense and defense teams.
To farm this achievement, get three friends willing to die three times each to your rockets. Kill them. It's as simple as that. If they cluster together, you can also try and farm the Tri-Splatteral Damage achievement as well. Thus, having a Kritzkrieg-equipped Medic healing you will help. Anything to increase your damage output helps in general, such as Jarate or the Buff Banner.
Note: This achievement is perhaps the most straightforwad in naming of all achievements. You simply dominate, as you are a dominator. No silly puns, no obscure references.
War Crime and Punishment
In a single life, kill 3 enemies who have damaged a Medic that is healing you.
If you are a Soldier, you are the second choice for a Medic, just behind a Heavy. This means that this achievement is not so hard to start, but may be a bit more difficulty to finish. Whenever an enemy damages your Medic, simply turn around and blow them away. Even if your Medic dies, as long as you killed the enemy, you will get the achievement. If you lose your Medic and get another while still alive, you will still get progress towards the achievement. Once you kill three enemies harming your Medic pals, you'll get the achievement.
To farm this, get a friend to play as Medic and another to play as another class such as Spy or Scout. have them damage or kill the Medic, then kill the enemy. Do this three times in a single life, and you'll get the achievement. Veyr easy to farm, and can be farmed alongside other achievements for the Spy, Scout, or Medic.
Note: Crime and Punishment is an excellent novel by the RUssian autho Fyodor Dostoevsky. It's his most well known novel, and revolves around an impoverished student killing a landlady and his subsequent descent into madness due to his guilt. A war crime, as mentioned earlier, is a crime against human rights done during a time of war, such as genocide or torture.
Spray of Defeat
Use a grenade to gib a player.
A taunt kill achievement! You must have the Equalizer to get this achievement. When you taunt with the Equalizer, you will throw down your weapon in disgust, grab a grenade, and blow yourself to pieces. This will automatically gib anyone near you. If you want to get it normally, just stand next to an enemy Sniper, and to farm just get a friend to stand still for you. It's just like every other taunt achievement, although the person doesn't have to be in front of you like other achievements.
Note: If you shoot a player performing this taunt before they finish, and they die as a result of this taunt, it will record as you getting a gib through the taunt. This can be used to get the achievement without exposing yourself to dying or having the Equalizer.
Guns of the Navar0wned
Kill 5 Engineer sentries while you are standing outside of their range.
An easy achievement, you must be standing within clear view of a sentry gun but outside of its range. This means that you can't shoot sentry guns around corners, as this does not count as outside their range. However, if you stand far away and fire so that splash damage hits a sentry around a corner, this will count. Since this is one of your class roles (distance sentry removal), you will probably get this achievement fairly quickly and painlessly. Easiest on wide-open maps.
To farm this, get a friend to build a sentry at a long distance. A good place is on the 2fort balcony. THen unload your rockets into it. Do this five times, and you'll get the achievement with no difficulty whatsoever. If there is a Medic that still needs it, this can be farmed alongside the Medic achiefvement to heal an Engineer whose buildings are under fire.
Note: This achievement is a reference to the book and film Guns of the Navarone, an exceelent World War 2 thriller revolving around a secret commando team infiltrating a German fortress.
Mutually Assured Destruction
Kill an enemy sniper with a rocket after he kills you.
This achievement is quite difficult, and you will most likely get it in normal play through luck. The best place to get this achievement is in 2fort, although if you are lucky you can get it elsewhere. You simply have to be killed by a Sniper while your rocket is in flight, then kill the Sniper with said rocket. Funnily enough, if doesn't have to be by the rifle or bow. Rather, the Sniper can kill you in any fashion, as long as your rocket kills him after you die.
To farm this achievement, damage a Sniper so that he is at low health. Stand far away and let him get a headshot on you as you fire a rocket in his direction. Then have him take the rocket to the face, gibbing him. You now have the achievement! If he is using the bow, he can also get the Sniper achievement to kill his killer after he has died through a bow.
Note: The concept of mutually-assured destruction is that two sides have such powerful weaponry that they can completely eliminate each other and possibly everyone else. It's used primarily to refer to the nuclear arms race that went on between the USA and the USSR.