In the comments, the developer has confirmed they will be restructuring achievements in the future, although there is no set date. This is great news, because some achievements have issues unlocking, and a redesign would fix that. Stay tuned for more info, and don't expect to keep a 100% completion forever if you're able to follow this guide to the letter!

With that in mind, let's start the guide--

These achievements are unlocked when you reach the main menu for the first time, while the game is still in Early Access.
Now that the game has left early access, these achievements are impossible to attain without using something like SAM. To all the completionists out there, my condolences.
Update:

In this game, there are multiple different gamemodes you can play. If you play each gamemode 100 times, you get every other achievement! Here are the gamemodes:

• Spidershot
  
• Reflexshot
  
• Strafeshot
  
• Pentakill
  
• Strafetrack
  
• Circletrack
  
• Blinkshot
  
• Ninjashot
  
• Detection
  
• Microshot
  
• Freetrack
  
• Audiospatial
  
• Capacity
  
• Decisionshot (currently bugged)

For each gamemode, there are achievements for playing it:

• 1 time
  
• 5 times
  
• 15 times
  
• 30 times
  
• 50 times
  
• 75 times
  
• 100 times

This will take a very long time, but there is no skill required in getting these achievements, only dedication and a lot of free time. Also, some of these achievements are bugged, so if one gamemode does not unlock achievements for you, try out a different one.

Many people have suggested in the comments that the achievements for Decisionshot are bugged. Unfortunately, this issue probably won't be fixed until the creators of the game redesign the achievements.

If you see something that isn't correct, or have an idea for new content, feel free to make suggestions in the comments, and I'll update this guide accordingly.

Thank you for reading, and have a fun time aiming!

~@craftablescience