Not really sure how to format these, so here goes; this is one of the most obscure handhelds I've actually seen in person, though I do not own it. It's based on the 1988 Namco arcade game of the same name and from what I can gather, it came out around the same time; you control Rick as you battle through three floors of monsters on a single-screen playfield in an attempt to save his girlfriend Jennifer. I've always found this game really fascinating for being an obscure entry in an already pretty niche series, though this does come at the cost of rarity & obscurity.
Below are some videos & articles about the game if this interests you:
West Mansion: The Splatterhouse Homepage - Splatterhouse: The LCD Handheld Game