We might be talking about different barbarian 2 games - there were two on Amiga and Atari ST. One was made by Palace, and was sort of like a very ugly flip-screen almost-fighting game (Barbarian 2: The Dungeon of Drax). The other was the Psygnosis game. It was a sidescrolling metroidvania game that looked like this:
Well - maybe we were talking about the same game, but those get confused a lot, so I had to make sure. Also - the Dungeon of Drax Barbarian game had two spiritual successor games released in recent years called
Age of Barbarian. The price is pretty steep and bizarrely for a small indie game it has an always-on DRM system, but it just looks like something I'd play just because: )