Impossibly Graceful Giant

This trope is brought to you by two giant robots doing the tango.

Humongous Mecha are a curious thing. By all logic, they can't work in the real world due to issues with weight distribution and speed. Even if such a machine existed, it would probably move something like Honda's Asimo — slow, clunky, and stuttering.

Apparently, nobody told this to Japan - watch any given mecha anime, and you'll see hundred-meter battle machines moving with the lithe, fluid grace of martial artists. Even more confusing: the pilot can pull off these amazing feats with nothing more than a pair of joysticks and a set of pedals. Why is this? Probably because, if the robots moved like the multi-ton walking tanks that they are, then the series would bore its viewers to death. A carryover from the Super Robot days considered too catchy to dismiss along with the humanoid form-- thus making this a rather obvious sub-trope of Rule of Cool. It often dissipates when a smaller character is in the scene, where from their perspective the machine is actually lumbering.

Kaiju tend to have the same problems, for similar reasons; you'd be bored if Godzilla throws an enemy and it takes 30 seconds between the start of its trajectory and it hitting the ground.

It should be noted that this phenomenon occurs almost exclusively in Japanese media; Humongous Mecha from Western sources tend to actually be big, slow, clumsy walking tanks (see BattleTech). This happens occasionally with Japan as well (see: Armored Core before the fourth installment, and of course, Steel Battalion).

It also should be noted that spider tanks can fall just as easily in this trope as humanoid robots, but rarely do. In fact, if a Mecha series has both you can expect that humanoid robots will move with much more fluidity than the multi-legged counterparts, even though logically the opposite should be true.

Can allow the use of a Motion Capture Mecha.

Often a form of Art Major Physics.

Anime & Manga

• In Gurren Lagann, the ganmen are piloted with nothing but a pair of handles. That's no big deal. However, when that mech pilots another mech using similar handles, which then pilots another mech using handles, which then pilots ANOTHER mech using handles, it gets ridiculous. Of course, in this series the Rule of Cool is a law of physics, so you should really just relax.
• Pictured above is from a silly little bit from Full Metal Panic it's subverted in that to do that it took weeks if not months to code all the movements to make it look fluid and it's further subverted when one of the Arm Slaves slips off at the end and crashes into some stuff.
• The Gundam Heavyarms, despite being the heaviest Gundam in its series, can do circus acrobatics just because its pilot can. Later taken to ridiculous heights when it does a spinning flip carrying four in-scale gatling guns.

Live Action TV

• Super Sentai and Power Rangers have embraced this more and more as the series' mecha fights have slowly shifted from People in Rubber Suits to CGI. Take the Delta Squad Megazord, which uses a lot of diving and rolling in its Gun Fu.

Film

• The Showa Godzilla series played this trope completely straight, as well some of the Millennium films, particularly Godzilla vs. Megaguirus and Godzilla: Final Wars. The Heisei series attempted to avert this as part of the filmmaker's attempts to make Godzilla Darker and Edgier. In lieu of the exciting battles seen during the Showa era, inspired by pro-wrestling, Heisei kaiju slowly waddle towards eachother, spew lasers back and forth, and when they're feeling really ambitious, will mix things up with some shoulder bumping. Fans complain about the fight sequences of the Heisei era to this day.