If you have multiple low level pets, go into any place with lots of mobs, kill some mobs, swap pets, repeat. All pets will gain Exp per mob killed while it is out, if enough mobs are killed, multiple pets can each level up at the end of the battle.
For high level pets, it is best to grind one pet at a time in solo Kraken with all characters on your account each day.
It is the best place for level >28 pets (if you don't have A Friend Once Lost unlocked, level >23 pets)
If you want more Exp per day for mid level pets, the next best is A Friend Once Lost (recommended for level <35).
A Friend Once Lost takes 55 seconds to clear and has unlimited runs, but it requires the story to be mostly completed to be unlocked. (Kraken takes 75s, Iset takes 90s, Shady Forest takes 60s, Cromm takes 40s) (This includes loading time)
It is the best place for level 1-28 pets, where levels 21-28 would be for single pet Exp. Since it has quite a lot of mobs, level 1-25 pets can use the pet switching method.
If you don't have A Friend Once Lost unlocked, the next best are Iset and Shady Forest but they really are relatively quite bad.
This is the summary, for more in depth details, read on.
Save Kraken for your high level pets.
If you do Kraken with a low level pet, it will gain the same Exp as it would have if that low level pet did something else. e.g. a level 15 pet will gain the same 2745 Exp in Kraken, Cromm, Shady Forest.
This is because each battle has an Exp cap. 5649 for Shady Forest, 3904 for Cromm, 35136 for Kraken. The level 15 pet has an Exp cap of 2745. The lower cap is used, so 2745 Exp is gained.
Apparently Kraken's Tentacles increase the Exp cap, so Cromm x9 (8 Tentacles + 1 Head) = Kraken Exp cap.
Bark, Lavasat still have a 3904 cap despite the extra things to kill, so prioritize the other S2 ex-raids and maybe even skip these.
Iset has a cap of 10061.
A Friend Once Lost has a cap of 7963-9595. (Depends on how many mobs you skipped/killed)
To expand on the pet switching method for low level pets, I'll use an example.
A Friend Once Lost can give up to 9595 Exp, but you have 2 level 16 pets which can only gain 3336 Exp and 1 level 5 pet which can only gain 306 Exp.
If you only have the one level 5 pet out the entire run, you will only gain 306 Exp.
If you only have one of the level 16 pets out the entire run, you will only gain 3336 Exp for one pet.
But if you summon the level 5 at the start and kill the cluster of spiders at the start. Then summon a level 16 pet and kill all remaining mobs up to the boss. Then summon the other level 16 pet just before the boss dies. After that one run, your level 5 pet will gain 306 Exp and your two level 16 pets will both gain 3336 Exp.
If you do not want to grind Kraken and only do raids, you can summon your pet at the end of the battle to gain Exp.
If you are forgetful, keep an invincible pet out the entire time and when you remember to, summon your non-invincible pet in the last few seconds. This way you don't miss out on Exp when your forget.
Pet Exp cap is reduced to 85.72% each in a party of 2. 78.56% in a party of 3. 75.00% in a party of 4. So if you are grinding an easy area like Kraken and want to level a high level pet (>42), it is better to solo. (For A Friend Once Lost level >24). The Exp cap is reduced even if someone does not have a pet summoned.
Note that party members affect Exp cap only, not the Exp you can gain. So if your level 40 pet (which can only gain 26068 Exp at most) will still gain 26068 Exp in a party of 2 in Kraken. But your level 48 pet (which can only gain 35136 Exp at most in Kraken) will only gain 30117 Exp in a party of 2 instead of 35136 solo.
All players in the party will gain the same amount of Pet Exp regardless of damage to the boss and how many mobs they killed.
Exp gained is calculated during the kill, so if someone dc before the kill in a party that was 4, it counts as 3 people.
Pet Exp is given even if a player is AFK the entire battle.
Pets can only gain 1 Level per battle.
After leveling, excess Exp is carried over to the next level. At very low levels (<5), it is not carried over.
Exp is based on each kill. So you can summon your pet in the last second and kill a boss to gain all Exp from that boss.
Exp gained is scaled to your pet's level. The higher the level, the more Exp you will gain.
All pets of the same Level gain the same amount of Exp and require the same amount of Exp to level up regardless of Rank, Type, Species.
Your pet will only gain Exp from kills while it is alive. If your pet already has Exp from killing mobs and then dies afterwards and stays dead, he will still gain Exp from those mobs that were killed before your pet died.
You can use "-" three times to hide and show the interface during the screenshots at the end of the battle, then use "Forfeit and Return to town" to instantly collect items and gain Exp for a relatively significant time save for fast S2 runs.
For Kraken, after using the Ballista, you can click "Forfeit and Return to town" so that the confirmation message appears, then when the screenshots are being taken, hit Enter.
It is possible skip the Ballista after killing Kraken, to do this, you need to use a multihit move onto two parts of the Kraken to kill and there will be a small chance for the skip to happen.
Level 50 is the level cap for all pets.
You need approximately 85 Krakens to level up a pet from level 40 to 50
You need approximately 134 Krakens to level up a pet from level 30 to 50
You need approximately 172 Krakens to level up a pet from level 20 to 50
You need approximately 202 Krakens to level up a pet from level 10 to 50
You need approximately 226 Krakens to level up a pet from level 1 to 50
Assuming it takes Kraken (75s), A Friend Once Lost (55s), Cromm (40s).
If you do level 1-20 in Cromm (40 min), 21-28 in A Friend Once Lost (30 min), 29-49 in Kraken (2h 53m), the total time is 4h 53m.
You need to run A Friend Once Lost 517 times to level up a pet from level 1 to 50. If you only run this, levels 1-30 takes 1h 33m, 31-40 takes 1h 49m, 41-50 takes 4h 31m, the total time is 7h 53m.