Elfen Lied is a 2008 free-to-play indie fighting game developed by KelvinBlue (presumably the David Mata Marin of Costa Rica mentioned in the game's start screen) using the freeware Beats of Rage engine. According to one playthrough, it was ported to the Sega Dreamcast, but a PC version exists as well.
Aside from a couple videos on Youtube, there is little footage of the game in existence. Download links are available on some emulator sites, but the safety and validity of these downloads is questionable, especially due to the amount of time between 2008 and the present day, and should be approached with caution.
The game begins with footage of hands pressing on and putting cracks in glass, apparently original artwork, then segues into a low quality version of the anime's opening theme song. Each stage features similarly low quality versions of the anime's scenes in between sections of 3D gameplay. The anime's scenes are also dubbed in Spanish with no subtitles. It appears to consist of multiple stages, but due to its difficulty, the other stages have not yet been shown or recorded.
The game sections have the player take control of Lucy, naked save for only her helmet, and the first stage has her fighting her way through guards, as well as Kurama, like she did in the first episode. Some guard models use heavier caliber guns than those from the anime, and some even ride motorcycles across the stage. Unlike in the anime, Lucy can take damage from their gunshots, as well as damage just from touching enemies that climb down into the elevator, and she only has a few vector attacks to hit them with. Her vectors only do a certain amount of damage instead of killing them in one hit, and Lucy can die as well if her health bar empties completely, requiring a start over if the player doesn't have any lives left.
At the end of the first stage, the player as Lucy must avoid being hit by a sniper, whose crosshairs follow Lucy across the map. If she's hit by the bullet, the section ends with the anime's scenes of Lucy being shot, falling off the cliff and into the ocean, then meeting Yuka and Kouta as Nyuu.