Animal Battle Aura

When a martial artist is extremely focused, an ethereal creature can be seen behind him, roaring, rearing, or screaming. Often used to show that the martial artist is mimicking something about the creature or (in more supernatural kung fu movies) channeling the trait from the creature. If taken less symbolically, the aura can accompany a powerful attack, be physically 'launched' at enemies to damage them, or surround the person generating it and mimic their movements.

A subtrope of Power Glows.

Examples of Animal Battle Aura include:

Anime and Manga

Naruto: The Kyuubi chakra is one such example, growing more defined as Naruto gets older and uses more and more of its power. The first time he taps into its chakra, his Battle Aura briefly forms an enormous demonic fox head above him before subsiding. When he fights Sasuke at the Valley of the End, it forms a semi-solid aura capable of attacking on its own, complete with ears, claws and a tail. Post-Time Skip, we see that he can sprout up to three chakra tails and still be (mostly) himself - if it gets to four, he and everyone around him is in serious trouble.
- Might Guy's Afternoon Tiger technique is a punch that compresses air into a giant tiger head.
- Naruto's complete Bijuu transformation is a Kaiju-sized fox Battle Aura.
Yachiru of Bleach has an angry cat aura in the show and some of the fighting games. Since we haven't actually seen her fight yet, this becomes her more powerful attacks.
- In addition, just before their last stroke, Ichigo's reiatsu manifests in the image of his Hollow mask and Zaraki's in the image of a skull. Both have lots and lots of teeth.
Rurouni Kenshin: Kenshin occasionally gets a dragon aura, and I think Enishi's had a tiger aura at least once as well.
Parodied in Ranma ½: the enemies stand with the auras of powerful beasts, with a LOOOOOOOOM sound effect. The heroes try to do the same with the auras of... girl Ranma at her adorablest, and an equally cute duck and pig, and a much smaller LOOOOOM effect.
Saint Seiya: Most constellations represent an animal or mystical creature.
Yu Yu Hakusho: Yusuke's aura manifests as a phoenix near the end of the Dark Tournament.
Parodied in Hayate the Combat Butler : Nishizawa's animal battle aura is a cute little hamster. Which causes Nagi to thoroughly mock her and nickname her "Hamster".
In Hajime no Ippo, boxer Sendo Takeshi's nickname is "The Naniwa Tiger". Try to guess what his battle aura looked like to Ippo.
Early in Parasyte, when provoked, the titular aliens project creatures behind them (a metaphor for their predatory bearing). One gives off a tarantula just before murdering a lion, and the main character shows a praying mantis before punching someone out.
Musubi from Sekirei has a bear aura, and all of her special attacks are bear-themed. The aura was even seen crying in a recent chapter when Musubi herself was upset.
Happens quite often to Zoro in One Piece, with a variety of animals depending on what attack he is using, from a dragon, to a bull, to a demon god...
When Yamcha from Dragon Ball uses his Wolf Fang Fist, he appears to take on the appearance of a wolf. Some of the fighting games replicate this imagery with a more standard Animal Battle Aura.
- Goku himself had a visible aura of his were-ape form when he punched through King Piccolo. Whether his movie / GT-exclusive Dragon Fist technique counts is debatable - in the movie it first appeared in, he briefly *became* a giant gold energy dragon, but in GT he would just as often simply summon it.
Natsu from Fairy Tail, when using a dramatic enough attack, will often be shown with a ghostly/flaming image of Igneel superimposed over him.
Captain Tsubasa's Tiger Shot, Falcon shot, Eagle Shot, and even Banana shot, which has monkeys dancing around in the series's games.
Beyblades with Bit Beasts have these.
Intimidations from Toriko. They coincide with the person's Game Face.

Film

In Shaolin Soccer, a goal shot goes so fast the ball bursts into flames, which then take the shape of a roaring puma. Undoubtedly as a parody of Captain Tsubasa.
- Later in the same match, the captain of Evil Team generates a black aura of such concentrated badness it takes on the shape of a demon before being sucked into the ball.
Parodied in Hot Rod where Rod calls upon animal spirits before his stunt jumps (most of which he fails miserably). The animals are almost completely random—for instance, the octopus and the house cat.

Literature

Harry Potter: The Patronus spell, a magical guardian created from good memories to repel Dementors, takes the shape of an animal. It usually represents either the person casting it or someone close to them - Harry's is a stag, representing his dead father's Animagus form - and can change form following an emotional upheaval.

Live Action TV

Use of the Animal Battle Aura is the Supernatural Martial Art taught in Juken Sentai Gekiranger/Power Rangers Jungle Fury. The Rangers can not only sic their auras on enemies, but give them physical form and make them Humongous Mecha.

MMORPGs

In World of Warcraft skilled hunters can aspect-dance. Switching aspects causes a sound to play and a picture to appear. Needless to say, frenzied aspect-dancing, while super-rare, looks really cool.

Tabletop Games

Exalted: The Anima Banners of Solars and Lunars are "iconic"—that is, at their brightest, they manifest as a coherent image that reflects on that particular Exalt's nature. For Solars, this can be anything—examples include symbolic animals, complex mandalas, mazes of ice, and many others. For Lunars, this is always their spirit shape, their default animal form. Abyssals also have iconic anima banners, but they tend to be more death-related imagery, and sometimes a corruption of the former Solar banner—skulls, corpses, wraiths, funeral shrouds, and the like. Green Sun Princes tend to have imagery styled after their Yozi patron, including demons descended from that particular Yozi. Alchemicals generally have industrial-themed imagery—machinery, electricity, smoke, steam, etc. Sidereals and Dragon-Blooded never have iconic anima banners (except a few Dragon-Bloods who have a representation of an Elemental Dragon), so this is one of the characteristics the Wyld Hunt uses to identify Anathema.
The Umbra auras of the Magic: The Gathering Rise of the Eldrazi set let you give any creature one, and impart some of the abilities of the aura's shape, along with a one-time protection from destruction.

Video Games

This is the big feature of Blue Dragon, basically.
Captain Falcon's Falcon Punch in the Super Smash Bros.. series is surrounded by a giant, flaming falcon.
All fighters in BlazBlue have a seal that glows behind them when they perform a Distortion Drive or Astral Heat. Not all of them are animal-themed, but this trope is in full force for Hakumen's wolf seal, Arakune's spider seal and Hazama's snake seal. Ragna's seal is the Black Beast itself.
Inazuma Eleven, which follows the concept of Captain Tsubasa, turn it Up to Eleven. As the matches in the game are almost as deadly as wars.
Sabin's Tiger Break Desperation Attack in Final Fantasy VI.
Employed in Osu! Tatakae! Ouendan!, during a particularly heated game of dodgeball.
A number of entries in the Tales (series) features the physical arte Beast, which sends a burst of spiritual energy in the shape of a lion's head flying at the enemy. Variations that use other animals like wolves or dragons also exist.
- There's also the Rising Phoenix arte, that surrounds the user with a fiery phoenix as they dive into the target.

Web Comics

Laika from Experimental Comic Kotone does this once to scare away some guys.

Western Animation

Ron Stoppable from the Kim Possible series finale does this when he goes into Monkey Mode.
Metalocalypse: Slightly subverted in the episode "Dethcarraldo". Dethklok takes a drug called Yopo that gives them visions of their animal selves, made obvious by the fact that the animals are anthropormorphic caricatures.
- Nathan Explosion is a crocodile.
- Pickle's the Drummer is an octopus (with much resemblance between the tentacles and his dreadlocks).
- William Murderface is a tiger (whose head is exactly the same).
- Toki Wartooth is a...um...rabbit? (Other than the ears and Toki's face, it's very difficult to tell.)
  - He's a rabbit, with feathers stuck to him.
- Skwisgaar Skwigelf is an owl (with the same blonde hair).
Justice League Unlimited uses this trope to represent Vixen's powers.
When Chiro from Super Robot Monkey Team Hyperforce Go! taps into the Power Primate, a giant green energy-gorilla forms around his body. When he pushes his abilities even further, he forms the aura and then pulls it back into himself.
"It soars through my mind like a beautiful bird..."