From the image I see you've managed to make that border, only in different color. But still, it's not hard proces to automate. If you have your image saved as 2D int array (talking about program, not filesystem) at some point, you can simply loop through and for every blank pixel with horizontal, vertical or diagonal non-blank neighbour make that pixel black.

But your output looks cool anyway ;)

PS.: But yeah, that solves only outside border. Borders at blends of characters with equipments are purely artistic choice and the only way to reproduce it with computer is to break these images to characters and equipment bits, then use multiple layers, make black borders around anything in each layer and then merge layers together.

Not suitable for actual conversion of images, but highly effective for image generators or in case someone wants to have these sprites in game with various weapons.