Slaughter Horse 2 is still in beta, and while I am still somewhat new to the game, the developer was gracious enough to fill in most of the information I was missing in the original draft. The guide is relatively complete, now.

I also wanted to note that the majority of the achievements are meant to cover truly worthwhile events and milestones, so Slaughter Horse 2 is not the type of game to expect to get all the achievements in. Just enjoy the game and have fun, but do know there are some achievements worth working towards.

Achievements cannot be earned while using cheats.

These achievements require you to complete games. Check out my Tips and Tricks guide for general information to help you win games.
Victory (Part One)
Win the game with a population of 20-28 ponies.
Victory (Part Two)
Win the game with a population of 30-38 ponies.
Victory (Part Three)
Win the game with a population of 40 ponies.
A Real Sew & Sew
Complete your cloak of many marks. I want to say this is easiest on a game of 24-28 ponies and 60 days just to be safe. I cannot offer specific strategies, but I know a few things:
1) The Undertaker must live so you can grab the cutie marks of council members who are lynched, or if the Changeling is killed by the Preacher.
2) Keeping the Mayor alive will help to reduce the frequency of lynchings. If multiple ponies are in the morgue, make sure to select the correct pony to get their cutie mark.
3) You must kill the last council member yourself; they cannot be lynched.
4) You must leave some Townies alive so that you do not win by the town surrendering while council members are alive.
The White Feather
Die a pacifist's death. You must complete the game without being responsible for a single pony death. It is advisable to take no actions for your pet or at night, and to only make friends or small talk at your shop. You are not affected if the Preacher kills the Changeling Spy.

These achievements require you to complete the game with a certain challenge enabled. These are only recommended for players who have already beaten the game several times. Unless otherwise noted, the general strategies for winning the game are useful, except you should not be trying to complete your cloak with any of these active.
Herbicide
Win a game with the Weedkiller challenge active. You will not be able to bake cakes. By far the easiest. You might have to be a bit more strategic with Death Letters, or you may have to play a slightly longer game to try and kill some of the difficult roles yourself. I highly recommend earning this and "Don't Get Familiar" at the same time. Potentially easier with a larger town.
Pony No Mates
Win a game with the Shunned challenge active. Your Friendship starts at 1 (and is difficult to increase). This plays like a fairly normal game, but keeping your Sanity high and Sus low are critical because your Friendship is going to be low the whole game. You probably won't be able to invite ponies over.
Don't Get Familiar
Win a game with the We Regret, No Pet challenge active (pairs well with "Herbicide"). This is actually relatively easy on a 40 pony town with the right approach. Shop: only use the "chat" option. Night phase: kill as often as possible. What works best is to pick a house and literally go around the map in a circle, attempting to kill at every house. Revisit houses that are blocked by any role, skip over houses where no pony is home. Loop back to the houses that were empty when you draw the Magician tarot card. Your three biggest threats are the disciple, veteran, and magician (which either tend to sort themselves out or you have a decent chance of surviving). You don't need to worry about the council members, as the town is so mad about all the murders that they are getting lynched left and right.
Spy Hunter
Win a game with the Spy Hunter challenge active. You have to kill the Changeling Spy in the first 9 days, but you will be granted with Sanity replenishment every night once you do. I'm not sure if this is the hardest challenge, but you will fail it plenty of times, as there is a decent amount of RNG involved. You have to be collecting intelligence from your shop and pet at every opportunity, and this is the only time that following up on partial address information is recommended. You will have to try and kill every night, either killing a known Townie (not Undertaker), or killing blindly. Usually, killing the Changeling is the only hard part, as you get a serious ongoing buff for doing so.

These are achievements that you will earn over time for playing the game, and achievements that are completely random chance.
Killing Ponies
There are achievements for killing 10, 100, 250, 500, and 1000 ponies in total. Only ponies that you have murdered, tortured, or that died from neglect count. You will get these as you continue to play the game. If you already have most of the other achievements, you can just play games with 40 ponies and try and kill ponies as fast as possible, skipping the pet and store phases.
Playing with a Full Deck
Draw all 12 tarot cards in a single game. Better chance in a town of 30-40 ponies.
All About Me
Read the Spy's secret file about yourself. Get lucky and kill the Changeling Spy, check which files they have, and then hope they have your file. This is easier in a game of 20 ponies.
The Trinity
Select all 3 holy prayers during a visit to church. Basically, just keep attending church and praying (pun intended) that you click the correct three (5% chance).
The Losty Legend
Your game generated "Pony Horse," the pony with the dumbest name in all the land. 100% RNG. This achievement is a reference to a famous clip of TheLostNarrator playing the original Pinkamena (now Slaughter Horse), where her and her friends lost it over a pony named "Pony Horse" who happened to be a changeling drone. The animation of this clip can be viewed below.
https://www.youtube.com/watch?v=gNLf1XPR4pY
You can earn this one somewhat intentionally by creating a new game with 40 ponies, saving and exiting, and then starting another new game (the game client usually crashes after doing this a few times). This achievement triggers on the Night Mare screen, so you can't miss it. I'm pretty sure the odds to get Pony Horse are something like 1/1000 or less, so even doing it the fast way can still take some time.

These require some amount of both skill and luck to complete.
I Fought the Law
Dispose of all three investigators (Deputy, Sheriff, Detective). This just means they all have to die before the game is over. You can usually kill one while the Magician tarot card is active.
Heartbreaking
Murder a best friend. You just have to become best friends (golden heart) with a townspony then murder them. You can usually invite them to your basement if given the chance.
Special Delivery
Write a full marks Death Letter. This must be a 5 skull Death Letter, friendship level is irrelevant.
On Your Knees and Bray
See the town hang the mule. The Mule is always earth pony. Just try to make earth ponies look suspicious, and at some point you'll hit the mule (and you will have to do this multiple times for Jinxed).
Secrets to the Grave
See your blackmailer killed. The Blackmailer is a special event that sometimes occurs during the game. They are selected at game start and are always a townie, so to improve odds of getting this event use a large town and try not to kill any townies!
So it's Treason, Then
Witness your Disciple turn against you. The Disciple will begin to get impatient once half the town is dead (i.e. on a 32 pony game it'll start after 16 deaths of any kind). Then, depending on your tarot draw, the Disciple will eventually turn on you, so best strategy is to kill ponies until you see signs in their letters they are getting impatient, then wait! If you have to kill because of bloodlust, make sure it is not a townie. Easier with more ponies.
The Master Baker
Bake all six cakes in a single game. This one may be easier in a game with fewer townsponies (at least I got it in a game of 20 ponies/30 days). You tend to get ingredients from killing and attempting to kill ponies, and from having your pet investigate houses. Just be sure to bake cakes whenever you can, and DO NOT send a pony the "Death by Chocolate" cake, as it will prevent you from baking any other cakes (baking it and holding onto it is okay). Just sort of lay low and kill only as needed to prevent bloodlust, focusing more on investigating houses and killing known targets (not blindly).
Crime of Passion
Kill the Mayor and their lover in a single strike. Canterday night is Mayor party night. Attack the mayor on this night and you have a good chance of getting this achievement.
Jinxed
Be the target of a Mule's curse. As aforementioned, you will have to see the Mule hanged several times, and you have to get lucky enough for the curse to target you (even though you cannot be affected).
None the Wiser
Torture a pony to death while the Royal Guard is stationed outside your house. You basically just have to get lucky enough to have the guard stationed after a successful kidnapping. You have a better chance later in the game if you can keep the Alicorn, Guard, and a friend alive, and at least one invitation. You also have two nights to kill a kidnapped pony, so try not to kill them the first night.
Escapology
Escape being hanged 3 times in a single game. Although your suspicion is the major factor in whether they decide to hang you or not, your sanity and friendship level with all those voting is also taken into consideration. Make friends and stay sane, and you'll dodge being hung much more frequently.
Friendly Fire
Cause the Veteran to shoot a friendly pony. You must send a Death Letter to the Veteran to make them go on high alert, and the Veteran has a chance to shoot and kill an innocent during the night. You can only do this once per game. You will get a message at the end of the night indicating that the Veteran is no longer on high alert if you successfully put them on high alert.

These are achievements that you can earn intentionally, and that you may not earn just from playing. Note: The White Feather falls into this category, but I wanted to separate achievements that actually required you to complete a playthrough.
The Witching Hour
Start a new game between 12:00 am and 1:00 am.
Signed, Sealed, and Delivered
Mention your own name in what is supposed to be an anonymous letter. You schumck. Include your selected name in a Death Letter; the effectiveness of the letter doesn't matter.
These Ponies Are Batty
Start a new game on October 31. Unless there is a trick I'm unaware of, you cannot earn this by manually changing your system clock's date to October 31; you must actually start a new game on October 31. Added in patch 0.13.
'Tis the Season
Jolly a pony to death. I believe this is just for killing a pony in the Christmas version of the game, usually available during December (not confirmed).
Trot of the Antarctic
Cause a pony to flee and die of hypothermia in the mountains. To do this, you must find the Reporter and send them all three of your Death Letters. They need to be reasonably scary, you will see in the Reporter's bulletins if they are working. Make sure to send all three in consecutive days to ensure the Reporter doesn't get lynched, or try to send them before the town has finished assembling the gallows. Note: I was successful when two letters had 3 skulls and one had 4 skulls.
Kitchen Nightmare
Look, you're just messing about. When trying to make a cake, put too many ingredients into the pot so they bounce out again, and do this over and over. All you need is three non-flesh ingredients, put all three in the pot, and keep trying to put the third one back in.