This Boss Stranger, also called the Greater Stranger, is a much larger and unique Stranger that serves as a mini-boss, the first of Parasite Eve II.
It is encountered by Aya Brea in the Akropolis Tower Café, where a young woman mutates into the monster right before Aya's eyes. It has double the hit points of a regular Stranger and is much larger, making it rather formidable, but still relatively easy as it is encountered early on in the game.
Due to its large size, the Boss Stranger is fairly slow, allowing Aya to use the tables in the café to take cover, if necessary. This is useful if Aya has to reload or wants to get some cheap shots while it's trying to find a way around.
When it's defeated, in order for the game to progress, the body needs to be searched in order to find the Implant. This causes it to get up before being killed permanently by Rupert Broderick.
Aya just before she encounters the woman in the cafe.