Rodge Rock in Retro Active is a shoot'em up and run-and-gun developed and published by Australian company Rodge Rock Software. It was released as shareware, and this video shows a playthrough of the shareware version. There is just one level in the shareware version.

According to this forum thread, the developer has lost the source code and the levels, so unless someone bought the full version back in the day and rediscovers it, the game is lost.

https://www.dosgames.com/forum/viewtopic.php?t=27451

You cannot jump in this game. Instead, you have a pair of rocket boots, allowing you to fly freely around. However, they have got a certain inertia and will gain a certain momentum. Rodge is equipped with a triple-shot pumpgun and black bombs. Collecting blue and black crystals will refill the ammo for one of them. The bombs can be thrown and will bounce off walls for a while. There are upgrades for the weapon to be found, which will increase the power of the shots and/or the number of directions for the shots. Rodge will loose health underwater, but he can find an oxygen tank to prevent this. Collecting hearts will replenish his health.