This achievement is for getting any one of your skills to rank 4 (expert). I got this myself in Chapter 4, you can get it earlier if you really wanted to, but you get enough skill points in the game to make this achievement pretty much effortless. (aka Technically missable, but you REALLY have to try for this).
Each skill point spent ups the skill achievement success percentage by 5%, so spend them immediately, as there is no reason to wait for enough to move up a rank as you get the benefit immediately.
In total, skills are really a minor part of the game, as they mostly give you a bit more information during investigations and unlock extra dialog options. Sometimes, they allow you to solve a puzzle one particular way (although there is always a solution that doesn't require a passed skill check). Occasionally, they will have affects on achievements. Therein, I'll list them below in order of "Achievement Importance":
Spot Hidden: Starts at rank 2 (and change). Get this to at least rank 3 as soon as possible and possibly higher, as it allows you to find hidden items needed for the John Raymond Legrasse Achievement.
As well as a few hidden occult objects for the Strange Secrets Achievement (example being the Sketch Book in Sarah Hawkins' bedroom).
Investigation: Starts at Rank 3. After you get spot hidden to 3, work on this one as well, as several items and achievements are locked behind this (sad pun: investigation allows you to successfully pick locks). The first achievement needing this is No Prohabition for Darkwater.
There are also occult items tied to this, the first one being the ssymbol drawings in the basket at the beginning of Chapter 4.
Another one tied to this is the Detective Historian achievement, as one of the books needed for this achievement is locked in a desk in Doctor Fuller's office in Chapter 9.
Occult: Start at rank 1, can only be raised by finding occult objects or assigning points to it in chapter one. Gives interesting conversation additions and investigation information, and can occasionally be used to lower you SAN score, while helps with the Fluent in R'Lyehian achievement and getting particular "difficulty" endings (possibly Nameless Cults, definitely Farewell).
Strength Starts at rank 3. Used for one early achievement -- The Delusional Investigator. Rank 3 should be plenty for this, so no need to raise it (and if you fail the check, you can use the dashboard method to try again). After this achievement, can be used to circumvent a few puzzles, but not really all that useful.
Medicine: Start at rank 1, can only be raised by finding medical books or assigning points to it in chapter one. Gives interesting answers Occasionally used to circumvent puzzles No achievements tied to this one so don't dump your chapter one starting points here -- your starter points are better spent elsewhere (namely: Occult, Spot Hidden, Investigation).
Eloquence: Starts at rank 2. Used to get more interesting information out of people or make them more cooperative (aka making puzzles easier). Most of the time, you can unlock dialog options through investigations that have a similar outcome, so not really needed.
As for starting points, I'd dump them all into Occult so that you can get that to rank 5 by end of game (plus you can only raise this stat by finding occult items). After chapter one and adding all your starting points into Occult, make sure to put at least enough points into Spot Hidden to reach rank 3 before you enter the warehouse. After this concentrate on raising Investigation and Spot Hidden. The other stats can wait.