New method found for extremely fast AP. This gets the achievement in a couple of hours.
This method can be started as early as Chapter 4. All that is needed is the Monster Whistle, which is given to you by Ardyn and Shield of the Just which is found in the tomb just ahead of the Secullam Pass Parking Spot. (Look for Thommels Glade on the Duscae portion of the map.)
It also helps having the nodes for Warp Factor and Warp Factor II unlocked.
Then go to the Abandoned Barn Parking Spot. (Look for The Three Valleys on the right side of the map.) Then just to the right of the Parking Spot you will see a rocky area with two Food Spots, a Mineral Deposit and a Treasure Spot.
Set your marker on the Treasure Spot and head there. Once you arrive you will find some Sabertusks. These are what you will be farming. Warp Strike them with the Shield equipped and they should all die from AOE damage. Depending on how many are spawned an AP pop up will show up telling you how much AP you received. Each monster you kill with the Warp Strike is 1 AP. Because of the Shield's AOE you should be able to kill the whole group on one Strike.
Now use the Monster Whistle and summon more Sabertusks. Repeat the process with Warp Striking and repeat with Whistle. The key is to kill the Monsters before the game starts a battle. That way, right after you Warp Strike you can immediately blow the Whistle again and repeat. It takes a few tries to get the rhythm down but after a few minutes the AP will start rolling in.
At night Giants will begin to spawn so head over to the Merrioth Haven southeast of the farming Spot and rest for the night. Bring some Elixer to replenish your MP when you get low if you don't want to wait for it to refill.
Video is not mine. Just posting for those who need a visual guide for the Shield and the farming spot. Here's a tip from evllmatt:
One note to add now that it's out- holiday dlc pack includes 2 particularly useful accessories: Warrior's Fanfare, and Blitzer's Fanfare. When used together, they add an ADDITIONAL 3AP after every battle, effectively doubling the results.