The Sims 4

Well, in addition to what was provided by the other guide (using books), you can also cheat your way into grinding this skill.

So, to do that,you need to do the following :
Step 1 : Press , it should open a command box on the top left corner of your screen, press
Step 2 : Type the following into your command box Traits.equip_trait SteelBladder and then press Start to gain the trait SteelBladder.
Step 3 : Now repeat step 2 but instead of SteelBladder, enter the following traits :
Needs traits : NeverWeary (Energy need never decrease), ForeverFresh (Hygiene need never decrease), ForeverFull(Hunger need never decrease), NeedsNoOne (Social need never decrease). The only need that will keep going down, depending on the skill you're mastering is the "Fun" one.
Useful traits : Savant (Helps learn skills faster), MorningSim (Helps learn skills faster in the morning)/NightOwl (Helps learn skills faster during the night), sadly only one of those two can be picked.
{I believe I have listed all the traits I used to master my skills but if I forgot some, I will add them later.}

Once you are done adding all required traits, you can click on a bar and select "Mix drinks" and then speed the game on the fastest speed and let your Sim level up its Mixology skill. Thanks to the traits, unless you have a job, you can go from 0 to 10 in one go.
Yes, its cheap, but since it doesn't disable your achievement, why not?

Hope it is useful! Please do leave your comments if you have anything to add.

There are 10 levels to learn. The mixology skills allow your sim to make drinks and entertain others while tending to the bar. They can earn tips while tending the bar. The Homey lot trait will give a sim a +50% gain skill boost if selected.

To get started, simply buy a bar from the buy mode or purchase the mixology books from a bookshelf.

The easiest way to max this skill out is to use the bar. It would take a couple sim days if the sim didn't have a job. The chef career requires this skill and one of the branches of this career is a mixology branch. So you could easily work on both maxing out the skill and maxing out the job.