There is a type of Lasagna at the Altissia Floating Market Station - Maagho (where you have the picture quest and have to talk to the guy there for one of the quests at Altissia) that you have to eat that gives you EXP boost, then you travel to past Lucis via Umbra (unlocked after getting to Altissia). The best way to do this is to go to the Hammerhead Rest Stop and traveling to Altissia via Umbra at the trailer near the Diner so that way, you'll be able to do this easily.
Step 1) After using Umbra, go to the Diner to trigger the Adamantoise hunt (must have triggered Adamantoise already from the quest Let Sleeping Mountains Lie from Cindy, where you flee from it)
Step 2) Run to the Adamantoise via warp or the stamina boost trick (pressing sprint when your stamina bar almost depletes)
Step 3) Warp to any place around the Adamantoise, using the Ring of Lucii's Alterna ability as soon as your MP is max (id suggest stocking up on some Ether just in case)
Step 4) Eventually, the Adamantoise will be sucked into the "void", granting you the achievement Tortoise Toppler, 50,000 Gil (10,000 gil per time afterwards) and 100,000+ xp every time.
Just rinse and repeat until the Lasagna wears off and then afterwards, travel to Altissia and stay at the Altissia Hotel (the 2nd person is the one you want to talk to) for 30,000 Gil which will give you 3x exp.
I started at level 60 and got up to level 100 in not even 8 hours (with breaks and such of course) using this trick
Source.