Mech Love, Not War Achievement
Mech Love, Not War20
Warmech is a rare monster that only spawns in a few locations. There is a 1/64 chance that you will encounter one on the 5th floor of the Flying Fortress, the same floor where you find Tiamat. Those odds of finding one are not exactly great; it's not wrong to assume that it will probably take over an hour.
Otherwise you can also find Warmech in certain puzzles of the Labyrinth of Time. This is much more ideal, since when you find the right puzzle, Warmechs are actually visible as patrolling enemies you are supposed to avoid, and you can fight them without having to look for random encounters. They are also weaker than the ones in the Flying Fortress, and give 8,000 experience when killed, making their puzzles the best places in the game to grind up the levels. The only con to relying on the Labyrinth to supply you with Warmechs is that the Labyrinth is randomized and it is conceivable that you could play all 8 times through and never get the correct puzzles. So, you take a chance whichever way you choose, but I tend to think your odds are better in the Labyrinth.
Note that Warmechs are much tougher to beat than ordinary random encounters. But since you only find them on your way to fight either Tiamat or Chronodia, you should have no problem.