Macross

Macross is a Japanese anime frnachise created by Shōji Kawamori.

Although this franchise is not directly about giantesses, the plot focuses on the war between human and alien giant humanoids (among which, there are giantesses).

Synopsis
The franchise features a fictional history of Earth and the human race after the year 1999. It consists of four TV series, four movies, six OVAs, one light novel, and five manga series, all sponsored by Big West Advertising, in addition to 40 video games set in the Macross universe, 2 crossover games, and a wide variety of physical merchandise.

Within the series, the term Macross is used to denote the main capital ship. This theme began in the original Macross, the SDF-1 Macross.

Overtechnology refers to the scientific advances discovered in an alien starship ASS-1 (Alien Star Ship - One later renamed Super Dimension Fortress - One Macross) that crashed on South Ataria island. Humans were able to reverse engineer the technology to create the mecha (variable fighters and destroids), faster-than-light space fold drive for starships and other advanced technologies that the series features. The first TV series was adapted into the first season of Robotech in 1985, with edited content and a revised script.
 * Source: https://en.wikipedia.org/wiki/Macross