I was going to suggest perhaps backing off the opposite-side cup first, so as to reduce the torque requirement in removing what looks like a damaged cup.

I've used alloy cups that had the driveside flange broken completely off, but would then be sure to loosen the opposite-side cup first, as one normally does anyway. The flangeless cup created an adjustable bottom bracket, no spacers needed.

The tool needed here is almost certainly a Shimano-pattern tool.

A long enough bolt with fine threads will not be the easiest thing to find if you do end up having to secure the tool to the cup to loosen it.

I've found such an 8mm fine-thread bolt from a seatpost clamp, but if this bb spindle is fully hollow, then a 6mm through bolt (or even 1/4" threaded rod) might be used with a nut (or nuts) to hold the tool firmly against/in the splines.
Park also makes a lower-profile spline tool (BBT-32) with a much larger through-hole in lieu of the 3/8" square-drive opening, and perhaps this will allow the standard crank bolt to secure the tool using a suitably-large fender washer (or bearing cone-type wrench with 8mm hole for hanging, as some have).

Likely bolting won't be necessary though, if you can hold the tool firmly and squarely to meet the cup while applying torque, use as long of a wrench as possible, tilting the handle slightly inward so as to eliminate any off-axis tilting force where the tool meets the splines.