The Elder Scrolls V: Skyrim Special Edition

Hitting level 25 should come through natural progression, unless you have no desire to do side quests (at which point, achievements don't matter really), but if you want to hasten this, you can easily do so with magic.

You'll need to obtain one, or all, of these spells (note, these are all novice skills and require 0 skill to be used)

Courage (Illusion) - Can be bought from Farengar Secret-Fire at Dragonsreach in Whiterun.

Oakflesh (Alteration) - Lucan Valerius of the Riverwood Trader sells the tome. Tolfdir at the College of Winterhold also sells the tome.

Equilibrium (Alteration) - This spell tome is found in Labyrinthian Chasm in the room with the Arcane Enchanter.

Healing (Restoration) - You start with this spell.

Once you have one of these, you must engage any enemy and find a spot where they cannot damage you. The best I have found is a Giant Camp just west of Whiterun. Continuing west, you'll see a bridge that you can get under, and the giants and mammoths cannot reach you,

Hide here and continue to cast any of these spells (you may need to get hit and actually heal for the Restoration skill to increase, I'm not sure). As you level up, increasing your magic helps and also refills your magic.

You can take a skill up to 100 in about 30 minutes if you effectively do this, having potions and a robe that quickens magic recovery also helps.

(video coming soon)

Simple solution for once you have reached High Hrothgar. Simply bring a weak damaging knife (I used an Iron Dagger) and find a Greybeard sitting in prayer. Then turn up the difficulty to legendary and sneak up behind the Greybeard and attack him.
Due to the high difficulty and the weakness of the dagger, they will not attack you in retaliation whilst you are undetected. This will send you sneak up at a fast rate.

To further increase the rate you level up, you can use the muffle spell to increase your illusion skill as well.

The Greybeard will stand up eventually, but you will be able to keep going. That said though, they will turn around after a while, so be careful as this will cause them to attack you, so regular quicksaves are recomended just in case.

Beyond that, Just keep going until your sneak reaches Lvl 100, at which point make your sneak legendary. Rinse and repeat until you hit Lvl. 25