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.
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Yggdra on a UFO.
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The hexagon outline can flash/glow to make it more obvious. Or the grid layout can be overlaid on top (maybe toggled).