This achievement is story related and will unlock automatically upon completion of Chapter 14. Spoiler free overview.
The chapter game play starts in earnest when Noctis interacts with the Hammerhead gate. There is an automatic rest at this point with a menu prepared by Ignis. So, if you have called Umbra and camped/rested and/or dined elsewhere, you start afresh once you pass the Hammerhead gate.
The choice of meal is significant because there is a mid-boss and two main bosses to fight. The path is relatively linear and following the objective marker will lead you to the mid-boss fight. When not engaged, you have the opportunity to save. Also, there are two rooms where you can rest and call Umbra. This is of value not only if you want to rest but also to Call Umbra. You can go back to Lucis where you can camp and dine. When you return to the present, you will have the boosts from the meal you ate in Lucis.
The mid-boss is vulnerable to Great Swords and immune to ice. Your best Great Sword would be a good choice for weapon. The mid-boss is also vulnerable to shields. So, Gladiolus's techniques--shield or great sword--can come in handy. I would recommend not using Armiger because it is best to have the Armiger gauge fully charged for the next fight. If you do use Armiger, though, you can use Call Umbra at the rest room and recharge the Armiger gauge in the past.
You may move directly on to the next fight or take a respite should you desire. You may want to make a manual save just before you engage. Note:
There is an achievement for beating the first of the two main bosses on Normal Difficulty. If you have been playing on Easy, go to options and change the difficulty to Normal. Alternatively, you can fight this boss on Easy and fight the boss again during post-game play on Normal difficulty to get the achievement.
When you are ready, follow the objective marker. This is the first of two boss fights. The boss is vulnerable to ice. So, an ice weapon is of value. Alternatively, Ignis's Enhancement technique can be employed. If triggered, Ignis will enchant Noctis's weapon with the ice element. Noctis's warp attacks provide lethal offense while ensuring his survivability. Employing Armiger can help you. The battle will also make use of two summons. One will occur automatically and the other is triggered to end the battle by pressing
The final boss is very evenly matched with Noctis who fights alone. However, eating the right meal can tip the balance substantially in your favor. So, it may be prudent to stop by the rest room, Call Umbra, and camp & dine in Lucis. The 100% critical hit rate provided by the Cooking Level 10 menu, Gold Tail Soup, will enable Noctis to decimate his opponent in about a minute. If this menu is not available, any substantial strength boost will help considerably. Also, you should have some Magitek boosters that eliminate magic costs for a short while. Their use will allow Noctis to pummel his opponent relentlessly with warp attacks and prevent him from composing himself for counters. Following the defeat of this boss, the chapter concludes and the achievement unlocks.Completing Chapter 14 unlocks Chapter 15 Post-Game play.
Chapter 14 is the last chapter of the main story. Upon completing it, the credits play out. Following that, you have the opportunity to make a save for post-game play. Upon loading this save, Noctis's party will be outside the rest room. The point in the story is after the mid-boss fight and just before the first of two main boss fights. You can call Umbra to go back to the past or you can replay your fights against the bosses. As stated earlier, there is an achievement related to beating the first boss on Normal difficulty so, if you fought him the first time on Easy, this allows you to replay the fight on Normal difficulty for the achievement. There are plenty of things to do in post-game play including acquiring weapons and fighting special enemies that are not available before post-game play.