Kung Fury achievements were unobtainable until today when the update and two DLCs came out, adding twice as many achievements. I have done my best to describe these achievements.
The free DLC contains no associated achievements, however you will need to buy A Day at the Beach to get every achievement in the game.
Lower priority achievements are obtained when higher priority achievements are gotten. And difficulty shows the time and effort it will take to get them.
This guide was written on day 1 of the update. I will update it as more details are available.

►This, as well as other defeat X amount of enemies are not achievements you should focus on. You unlock them over time by playing the game.
►This, as well as other defeat X amount of enemies are not achievements you should focus on. You unlock them over time by playing the game.
►This, as well as other defeat X amount of enemies are not achievements you should focus on. You unlock them over time by playing the game.
►This, as well as other defeat X amount of enemies are not achievements you should focus on. You unlock them over time by playing the game.
►This, as well as other defeat X amount of enemies are not achievements you should focus on. You unlock them over time by playing the game.
►K.F has the highest score in the game. This achievement is your biggest goal in Classic Mode.
►Recommended Characters: 1- Hackerman / 2- Triceracop / 3- Barbarianna
►Since K.F's score is higher than Hackerman's, you will get this achievement automatically upon getting the highest score.
►You should get this achievement while trying to get the highest score.
►Recommended Characters: Kung Fury / David Hasselhoff / Barbarianna
►K.F and Hasselhoff are functionally very similar, and easier for newer players. Barbarianna can one-shot harder enemies. Hackerman and Triceratops are not recommended, since they are the hardest and easiest to miss with characters.
►Simply spam one direction until you find the building with Hasselhoff's poster, intentionally take damage and die in front of it.
►Hardest achievement in base game, requires you to intentionally miss 150 times. Missing should be your main goal.
►Try to avoid enemies in one direction while continously spamming the other direction.
►Recommended Character: 1- Barbarianna / 2- Kung Fury
►Hackerman is too slow for this, and while Triceracop has enough health to survive, clearing the enemies is more useful than survival. With Barbarianna spam one direction and whenever you can clear the enemies on the other side with the finisher.
  ►One of the easier achievements, simply spamming one direction will get you the achievement. You are also likely to get this during "Excuse Me Miss" achievement.
  ►Recommended Character: Kung Fury

For this set of achievements, you will need to beat the DLC as each character. You only have to beat the last chapter, which is the boss, as the active character. Here are some tips to optimize these set of achievements:
►First, play through the DLC with your character of choice. If you are playing singleplayer just play solo, it is not a long DLC. After Beating it with your character of choice you will get the achievement.
►After beating the boss, go back to the start and select the DLC, this time press Start on another controller (You can use Keyboard Player 1 and Controller as Player 2).
Now press "W" to warp the the final stage. Warp code is 5 / 5 / 5 / 4 / X.
You will play as the first character and Player 2 will stand still on the left side of the screen (choose the characters you haven't beaten the boss with).
This makes the fight easier by giving you 2 extra lives for the fight. Now when you beat it, you will get two achievements instead of one. Do this again with the 2 remaining characters and you should unlock 14 achievements in total.

►Simply beat the boss as Kung Fury. Follow the tips above to optimize and save time.
►Simply beat the boss as Barbariana. Follow the tips above to optimize and save time.
►Simply beat the boss as Hackerman. Follow the tips above to optimize and save time.
►Simply beat the boss as Triceracop. Follow the tips above to optimize and save time.
►Simply beat the boss as Hasselhoff. Follow the tips above to optimize and save time.
►For these achievements you just have to go through the DLC. You do not have to play them again since you can warp to the boss.
►For these achievements you just have to go through the DLC. You do not have to play them again since you can warp to the boss.
►For these achievements you just have to go through the DLC. You do not have to play them again since you can warp to the boss.
►For these achievements you just have to go through the DLC. You do not have to play them again since you can warp to the boss.
►For these achievements you just have to go through the DLC. You do not have to play them again since you can warp to the boss.
►For these achievements you just have to go through the DLC. You do not have to play them again since you can warp to the boss.
►This is the last stage in the DLC, expect high difficulty.
►Sometimes enemies will come out of breakable objects, make sure you break the objects as soon as they enter the screen.
►Glitched enemies only appear in "Virtual Stage". If you do kill enough enemies in the automatic segment, you will need to go back and kill more.
►Unlocked upon beating the final boss with one character.
►Unlocked upon beating the final boss with two characters.
►Recommended Characters: Triceracop / HackerMan. Having ranged attacks will make this achievement easier.
►For this achievement you will need to finish off the boss while it is "invulnerable"
►When you use your special, the boss will enter a vulnerable state, lower the boss' HP until there is very little left.
►If you attack without using your special, you will actually deal 1 damage. For this achievement, you will need to finish off the boss with said 1 damage, just by spamming it when the boss is at low HP. (You can use your special to get the boss to low HP, just do not finish it while it is stunned)

Check out my guide on all the warps for the DLC.
https://cs2bus.com/sharedfiles/filedetails/?id=2655863487

Hope this was helpful.