I'd consider a free-roaming tiled 2D environment (e.g. Bomberman) instead of a constrained side-view one: the turtle can only walk on the lower floor, so enemy-only platforms are quite pointless.
An overhead perspective wouldn't affect tubes and plumbers much and it would allow the turtle to shoot in any direction for added tactical depth (turn while moving and shoot forward; maybe shoot something different backwards with another button).
The turtle should be moving at turtle speed: the marksmanship that makes constrained movement and fixed-direction shooting with a single bullet enjoyable in games like Space Invaders should be out of the question, so I expect the object of the game to be astutely combining movement and close-range shooting to kill plumbers and hold back tube growth; it should certainly be easier to accomplish with a greater choice of movement and attack moves and with more nuanced enemy behaviour than passing overhead, laying tubes and shooting down.
- Pickup items (again, like Bomberman): bouncing shots (particularly if they can be fired obliquely) and ways to destroy tubes (maybe a limited-use helmet for head butts) would be particularly useful upgrades.
- Fixed hazards, e.g. pits.
- Flooding the map from the tubes, tile by tile.