You can do all these after the story if you want. (You cannot get to some of them before you have basically finished the story anyway.)
* <-- For the RNG ones, if it is not there, fast travel to the area again to reset the area and look again.
The images are probably way too big for people on their phones as I got them from my Xbox so I apologise for that.
Rohlan Fields
Tak the Yak
Mimic
*Leaping the Frog
Kortara Mountain Range
Dwelley of the Valley
Gol D. Waterfly (Kill a lot of waterflies in the south-east area first)
Fiorwoods
Ekskalibur (run around the trees a few times)
Arthros (need to kill Ekskalibur first)
Flower Fields of Perpetua
*Da Capo (Enter/Exit cave)
Humphry the Hungry (Follow sand shifts)
Arkant Archipelago
Otter Nobunaga (Remove armor from party before you enter Arkant Archipelago) *Thanks, devilawakens32
Hairy Otter (Need magical users in party. I had Magnolia, Be'thraz, Amalia and Lenne) *Thanks, devilawakens32
**Victor also works as well. Thanks, Soviet Blues.
Shambala
*Golden Borb Bob (Have 100,000 coins on you)
*Aurora the Dragon
Organe Grottos (Late game)
(Need elevator key for Raminas Tower, so you can get some berries to kill these invincible Tadeye monsters! and reach Bog the Real Gob. Elevator key is from the office of the Academy of Nhysa. Thanks, nine3cubed.)
*Senior Tadeye (removes all other enemies when it spawns. Use the fast travel crystal in this west area, go right to the climbable wall, pan camera up to see if the normal enemy spawned)
Bog the Real Gob
(Complete quest: A Goblin's Dilemma, Go to goblins village in Ornate Grotto (North-East), Buy book from goblin merchant to understand them, talk to goblin on the top right, pick up miner key near merchant, travel to Rockbottom, enter mine and follow path right until you see a door you can enter.)
There seems to be two story related characters listed in this section of the Bestiary so I will include them below