Chaugmar switches between forms. You can just default 2 or 3 turns then he opens his eye and then you can wail on him. He's probably the easiest of the 4 crystal bosses.
Which is fair since I hate how you have to go through Mythril Mines,Underflow, and then the Fire Temple just to fight him -.-
Also Dat New Years Nemesis was the THE hardest boss ever. Moreso then anything else in the game. Beat Be Mine; White Fox kinda easily thanks to that High Jump strat I posted but the New Years one? Holy crap. Here's how I beat him.
He's the fastest boss ever released so you need a TON of speed gear to out speed him.
3x Time Mage/Bushidos yes, Bushido.
1x Performer/Spiritualism
Gear:
All of them need x2 Falcon Knife(Norende 11 special weapon shop)
and for accessory's Hermes Shoes
rest you can put in MATK+ and INT+ gear
Abilities:
For the Time Mages Speed+30 and Speed+20%
For the Performer Speed+20% Hasten World
Strat:
Mages Bravex4 use Bushido's Free Lunch then x3 Meteor
Performer x2 Brave Love Rush then Stillness
How it works:
The Mages will be faster then everyone on the field and will be able to cast 3x Meteor for no Mp cost. The performer will not outspeed the boss the first turn but after a Love Rush it will. Stillness lets you not take any dmg while waiting for Hasten World to give you back the BP to start the cycle all over again.
This is an "auto" strat you can use for more bosses just set it up and hit auto and walk away.