Well, just in case this problem was assigned to you as part of your Phd. thesis research, :-), I would say, that for a bullseye, switch to a radial coordinate system. So set up a grid to print, say an array of arrays, AOA's. Say you had an array size of 80x80, for array indices 0..79.

So at (40,40) you would setup your origin for your radial coordinate system, where every position is defined by a reference angle and a radial distance to the object.

So, start filling in your array blocks with your characters, starting at the center, and blossoming outwards. So you determine at that any given position what the radius is to that cell, and if the radius is in certain ranges, they get assigned different characters to that cell.

But, I won't say more, as it might influence you too much. The radius can be easily converted to cartesian coordinates with some simple trig.

P.S. For mucho bonus points, how might you implement a 3 dimensional bullseye?