The Commodore 64 version of the game, while also titled Daredevil Dennis on the cover, is subtitled "The Sequel" on the title screen and there are significant differences. It now includes a backstory claiming Dennis is a former movie star who was awarded an Oscar in his heyday. His cousin Decidedly Daft Douglas has stolen his Oscar, cut it into small pieces, and hidden them in various places around the movie studio's storerooms.
Each level takes the form of one of the storerooms. The levels are now in two parts: an introductory mini-level and the proper level. In the mini-level, Dennis walks to the studio through a meadow. During his walk, he can jump to avoid trampling flowers, and to burst balloons, for bonus points. The mini-level is completely safe and ends after a timer runs out.
The proper level plays very much the same as the BBC/Electron version. Dennis rides across the storeroom's various platforms (although his only vehicle is now his motorcycle). As well as avoiding hazards, pieces of the Oscar drop down from the sky in parcels. The parcels open upon reaching a platform, revealing an Oscar piece, which Dennis can then collect. An extra life can be had by completing an Oscar, after which the Oscar restarts from scratch.
Another extra feature in the 'sequel' is "porridge power". Every morning, Dennis eats porridge for breakfast, which gives him a finite amount of "porridge power". This can be accessed by holding down on the joystick, which will make Dennis invincible for a short time
Source: Wikipedia, "Daredevil Dennis", available under the CC-BY-SA License.