there are a total of 25 achievements some of which are very straight forward and others are a pain to get, for the easy ones you can simply finish the game on easy difficulty and get them and since the game is only bearable for one play through you can get the rest by some registry edits.

these one are straight forward, you just collect the requested amount of stars. levels ranges from having 50 -100 stars so for the Star Guardian you need to finish 5 or 6 levels at least.

(tho not tested the registry edit might help with getting these easily as well)

1. Star Collector
Collect a total of 10 stars.
2. Star Master
Collect a total of 100 stars.
3. Star Guardian
Collect a total of 500 stars.
4. Star Hunter
Collect all stars on any level.

just kill the zombies, you should get all 3 in your first play through.

1. Zombie Hunter
Kill 10 zombies.
2. Zombie Crusher
Kill 75 zombies.
3. Who is the Prey Now?
Kill 200 zombies.

these ones are a bit hard to achieve but still manageable in one playthrough, you just have to not waste zombies. zombies are usually close to the different types of traps and need a bit of push, you can do that by dashing or ground slamming next to the zombies to throw them into the traps.

(the arrow trap is hardest to get)

1.Master the Stone
Get 10 zombies to be squished by the stone traps.
2.Master the Axe
Get 10 zombies to die by an axe.
3.Master the Fire
Get 10 zombies killed by the fire.
4.Master the Cannon
Get 10 zombies to die by a cannon.
5.Master the Saw
Get 10 zombies to die by the saw trap.
6.Master the Arrow
Get 10 zombies killed by the arrow machine.

these are easily achieved in the first play through

1.One Step Into the Adventure!
Finish the first level.
2.Learning to Dash
Dash through zombies 10 times.
3.Dash Master
Dash through zombies 100 times.
4.Learning to Ground Slam
Slam the ground and hit a zombie 10 times.
5.Ground Slam Master
Slam the ground and hit a zombie 100 times
6.Zombies are Stupid
Make the zombie that charges you hit a wall.
7.Heal me Instead
Get the medic zombie to heal you for 100 total health.
8.Hawkeye
Hit the crazy zombie with the bombs with a bullet.

as mentioned in the intro you can make these ones easier to achieve by a registry edit. all you have to do is open the registry editor(pressing "Win+R" and then typing "regedit") and go to this location:
HKEY_CURRENT_USER\SOFTWARE\DefaultCompany\SpaceeZombies

• there you will find some entries names "Level##StarsCollected" which is number of collected stars of thier respected level, you can change all of them to 100 to get 3 medals on all levels and get the "You are Amazing" achievement
  (this could also give you the 4 star collect achievements but I haven't tested it, post a comment if you have)
  
• the other entry that you can change is "LevelComplete" which is the number of finished levels, you can change the number to 12 to open all levels and then you have to finish the last levels to unlock the achievement for that difficulty

1.You Saved the World!
Finish the game on any difficulty.
2.You Saved a cruel World!
Finish the game on medium difficulty .
3.You Did the Unimaginable!!!
Finish the game on hard difficulty.
4.You are Amazing
Complete all levels with 3 medals.