The Gentle Step Twin Lion Fists is a high-level secret Gentle Fist technique taught only to the main branch of the Hyūga clan.
The user changes the shape of chakra released from both hands into large guardian lion-shaped shrouds. Doing so greatly increases range and destructive power. The lion heads drain the chakra network of those they touch. It is an extremely difficult ability to learn, as the slightest mistake in chakra control will lead to failure, meaning it is a feat requiring the Byakugan. This technique can be used in conjunction with the Eight Trigrams Sixty-Four Palms.
In the anime, it is shown that during some time in Part II after learning from Ino of Naruto's new technique, Hinata trained with Neji to develop her own. By expelling chakra from the tenketsu as an innate ability exclusive to the Hyūga, and after using precise chakra control, Hinata was able to shape the chakra around her fists in the form of blue guardian lions, as witnessed by both Neji and Hanabi.
In The Last: Naruto the Movie, Hinata first tries to destroy the Tenseigan orb with the upgraded version of this technique but doesn't inflict enough damage to destroy it. Then she proceeds to combine this technique with Naruto's Rasengan at his request and finally manages to destroy it.
In Naruto Shippūden: Ultimate Ninja Storm 2, to execute the Gentle Step Twin Lion Fists, Hinata hits her opponent multiple times with her palms, pushing them back. Then she forms the guardian lion heads and slams them into her opponent, where they explode and send the opponent flying back.