Zortch (Maxinum Against the Alien Brainsuckers) is a charming N64-styled shooter featuring 20 levels spanning five episodes and a total of 6 achievements.
Since the said achievements are rather meta compared to ones from similar games, discovering them on one's own by taking cues from the relevant icons and descriptions is highly advised. Still, this guide provides clean-cut pointers for getting them all in case you miss some along the way.
The guide lists them in order of 'first chance of unlocking' and categorizes them into three levels from the first episode. Note that any previously completed level can be replayed via 'Level Select'.

These two can be done any time on any level, yet are listed under E1M1 to keep things simple.
Click on 'Help' from the main menu and get a crash course in basic mechanics.
Drop down the console via the tilde (") key, type in iddqd[doomwiki.org]and press enter.
Tough luck! If you are in need of working ones, try: bee, guthood, lab and runandgun.

These two are related to Pugon Pistol and the tripmines.
Assuming you already have a Pugon Pistol, grab the first batch of tripmines from secret #5:
Create a ballistic shield by alt-firing Pugon Pistol and plant a tripmine on the said shield:
Following on, get close to the planted tripmines found right after the stairs and steal one:
Interestingly, this achievement can also be unlocked while watching the pre-recorded demos that are looped in the main menu, in one of which the dev utilizes the mechanic in question.

These two can also be done on any level that contain a Brainsucker as a regular enemy.
Wait for the boss' projectile attack and counter it with a kick. Then, be on the lookout for another projectile and send it back by using Multi-tool's alt-fire this time:
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Zortch26 (rated it 1 out of 5 stars): aliens tried to eat my brain :(