No video codec hardware, no storage for video files (cartridges max 8 MB).
CPU (Sharp LR35902 @ 4.19 MHz) far too slow for decoding.
Game Boy Color (CGB-01): Barely
Color screen, same resolution.
Homebrew "Game Boy Video" cartridges existed (e.g., Pokémon Anime episodes, ~10 min, 15 fps, heavily compressed). Required special cartridge + PC software to encode. Not user-loadable.
Game Boy Advance (AGB-001) / SP (AGS-001) / Micro (OXY-001): Limited
240×160, 32K colors, 16.78 MHz ARM7TDMI.
Game Boy Advance Video cartridges (2004–2005): Licensed carts with 45–90 min cartoons (Nickelodeon, Cartoon Network). ~$20 each. No user content.
Homebrew: Retro-Go (CFW) can play low-res video (128×96, 10 fps) from SD via flashcart. Not practical.
Real Solution
Use a smartphone, tablet, or dedicated media player. Even a $30 used Android phone plays 1080p video for hours. Game Boys are for games.