Tales of Vesperia: Definitive Edition

Since the achievement doesn't specify, what you have to do is complete the game in under 15 hours to unlock this achievement. The achievement will pop during the end credits of the game, but I skipped over everything so fast that the achievement popped on the post game Save screen instead.

The 15 hours starts from the end time of your last playthrough. So if I had 139 hours played on my previous file and start my speedrun with that file, you'd have to complete the game before the time hits 154 hours. Note that time keeps running even if you're in the menu screen, but doesn't keep running if you pause the game.

This should be done on a New Game+ file or further with GRADE bonuses unlocked. The ones I used were: 99 items, 10x EXP, Items, Skills, Artes, 1 SP per Skill, Gald and Synth Level. You need around 11k GRADE to go overboard on this achievement. Honestly though, you could easily complete the speedrun with transferring just your Items and maybe nabbing the 99 of each item GRADE perk so you don't have to waste time going to towns to buy more holy bottles. Grabbing the Synth level is highly recommended too (see below).

If you transfer your Synth Level, you can craft the Winged Boots immediately at the first merchant in Zaphias before you even hit the tutorial fight. This speeds up the beginning phases of Arc 1 immensely. Otherwise you have to wait till you hit Dahngrest to forge the boots, which is why I recommend buying the Synth GRADE perk for the speedrun.

Turn your difficulty down to Easy and simply power through the whole game. Use holy bottles to skip every fight. Don't do sidequests. I used about 10 holy bottles from the start of the game to Capua Nor, then restocked to 99 Holy Bottles there using the Gald from my previous playthrough. I ended the game with about 45 Holy Bottles left without ever hitting another merchant.

Make sure to skip every "talking" cutscene by pressing then pressing .
Hold down + to fast skip text in specific cases where you can't skip text scenes, like with Alexei or Duke.

If you get to Barbos by 4:00ish and Alexei by 8:00ish, you're on track to completing it on time if you're worried about your speed.

I completed the game in 4 Hours and 22 minutes with some detours and slight mess ups. I hit Barbos at around 1hr 13min and Alexei at around 3hours 10 min.

You can also use the free DLC packs to gain a bunch of levels right off the start of the game which, combined with your Items GRADE perk, will carry you through the entire game (especially if you are playing on Easy).