Gridless is too hard. Optimal path is to curve around enemy bullets if possible, and you need a program to curve around for you for max distance. Too much to deal with for the player. How about a hexagonal grid, then?
A UFO (not to proportions). The hexagon is the hurtbox.
![IPB Image](http://i.imgur.com/zuNCyKn.png)
Yggdra on a UFO.
![IPB Image](http://i.imgur.com/K1ROfqF.png)
The hexagon outline can flash/glow to make it more obvious. Or the grid layout can be overlaid on top (maybe toggled).