Treasure Island Dizzy is a computer platform/puzzle game published in 1988 by Codemasters and was released on multiple platforms.

This was the 2nd game in the Dizzy series.

This is a short sample of the C64 version.

More info:
https://en.wikipedia.org/wiki/Treasure_Island_Dizzy
https://www.mobygames.com/game/treasure-island-dizzy
http://www.yolkfolk.com/site/games.php?game_id=2