Puk have many odd traits.

Wind-based spells, wind-based weaponskills, added-effect wind damage weapons, and Detonation skillchain damage will heal rather than harm a Puk.

On Lightsday, Windsday, and during Light or Wind Weather, Puks have the ability to regenerate TP. This can cause massive spamming of TP moves.

If you cast a spell of the element corresponding to the elemental day of the in-game Vana'diel day on a puk, it will get 100% TP instantly.

Wind Shear will knock you back a good distance. Make sure you are not tossed into other aggro monsters.

If you hunt White Wind in Camp #1 when you can use it, you will need a small group able to kill the NM.

 The NM Puk Waugyl is a good Puk to learn White Wind from. 

Zone into Abyssea - Altepa and get your time, and Atma/Abyssite buffs. Use the Conflux and warp to #4, and walk down to the camp circled in red on the map above. Here you can spawn Waugyl by trading the item 'Puppets Blood' to the ??? that is located at F-9. If you need to farm the Puppets Blood, it drops from the Desert Puks, that are a bit farther south of the camp.

Waugyl can be duoed by a 90 DNC/NIN and another Damage dealer, and there are reports of 90 SMN, and BST being able to solo it. The two big issues are ill wind, which can do a lot of damage, and that the NM has a lot of HP and uses White Wind to heal itself often. Stunning Ill wind is not hard, and solves that problem. Being able to deal large spike damge via WS, Skill Chain, or spells is key in killing the NM in a reasonable period of time. If you cannot put out the damage, you'll stalemate and eventually get killed by an unlucky series of ill Winds. But a skilled evasion/shadow based tank (DNC, NIN, THF) with healing support, can keep at it almost forever.

If you bring a small party of 90's, Stun Ill wind, and take care, no problems should be had.

New Puks that use White Wind were added to the Boyahda tree in the circled location (F-9) of the map above. They are IT to a level 91 player, so are probably close to level 100 and are very nasty. To make things extra fun equally strong crawlers and a Thunder elemental are all over the close area where you might fight, and getting their attention can kill even a full level 90 party.

If you chose to hunt here, know that casting an elemental spell that matches the day will instantly give the Puk 100% TP, so getting it to use the move will not be a problem. A good traditional EXP party can handle these with difficulty. The aggro issues make this a very annoying camp.

White Wind can be learned in a Mamool Ja Besieged. You, a party, or alliance member must get the killing blow on the Puk for a chance to learn the spell. You do not need to have had engaged the monster yourself to learn the spell. 

A level 90 BLU can solo one of these mobs.