Warmech is an enemy located in the Flying Fortress on the final floor where you fight Tiamat. There is a 1/64 chance you will encounter him there, however it is highly recommended that you do not even attempt to fight him here. Instead, wait until you are working your way through the Labyrinth of Time as there are two or three challenges there where you can encounter many of them and by the time you have reached this stage they will pose no where near as great a threat as they would have should you choose to fight them too early, while it is still doable it can take a couple of hours to encounter Warmech, let alone worrying whether or not you will defeat him.
Warmech's Stats:
HP - 2000
Attack - 128
Int.- 50
Defence - 80
Magic Defence - 200
Agility - 48
Accuracy - 200
Evasion - 96
My party when I did this was Knight (Fighter), Master (Black Belt), White & Black Wizard (Mage). First off use Giants Glove with your Knight, White Robes (Invisira) with your Master, your highest Heal spell (note not Cure spell) with the White Wizard and have your Black Wizard cast Haste on your fighter. Have your Fighter attack from now on, your Master use the White Robes at least 5 times to make dodging Warmechs attacks more likely and increasing chance for survival. Your White Wizard should be constantly casting either Healaga if the group takes damage or Curaja if a single person is hit and Life/Full-Life if someone is KO'd do not waste a turn doing anything else with her. Have your Black Wizard cast Temper repeatedly on your Knight to boost his damage. Once you have lasted a few turns and you feel your defences are sufficient, have your Master use the Giants Gloves and have your Black Wizard start buffing him with Temper as well, you should have Warmech defeated in no time, unless he decides to be a douche and use multiple Nukes in a row.
If you head over to my other solution -
Solution for Out of Time In Final Fantasy (WP)You will find a link explaining all the puzzles in the Labyrinth of Time. If you just want to know what puzzles have Warmechs in them simply hit Ctrl+F to activate the search function and type Warmech into the box and you should be able to easily locate it.
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If you have any good strategies for different party setups, either comment or pm me and I may add them to the solution for people using similar tactics.