To get this achievement you must first, brew an 'advanced potion of strength'. To brew this you will first need a brewing stand (crafted using 3 cobblestone and 1 blaze rod). When you have your brewing stand, make sure to craft some glass bottles (3 glass), fill them up with water, and place them in the stand.
Once you've done all that go into the brewing stand menu and add nether wart to make an 'awkward potion'. Then, add 'blaze powder' to make Potion of Strength. Finally, add the glowstone dust to make Potion of Strength II.
Now simply go outside at night, drink the potion, and hit a monster with a Diamond sword. The achievement should then pop. If you are stuck or unclear on a step, leave a comment and I'll get back to you soon.