Honestly, the easiest way to make armor piercing ammo that I've found was to insert tungsten rods into hollow point bullets that have been drilled out a but. Sheerly for amusement's sake, but it did a heck of a better job at piercing mild steel plate and did a better job on ar500.
Basically took a 40 grain blitz king, and carefully used a Dremel to drill out the centre. I then used my loading press to carefully press in a piece of tungsten rod. Surely it wasn't accurate or precisely done, but I could hit a 4x4 plate at fifty years and most of the time a 6x6 plate at a hundred.
Went straight through 3/8" plate at 100 yards, and 1/2" at 50, didn't bring enough to try out a lot of various situations though. The ar500 took a good sized chunk out, but didn't penetrate even at about 30 yards (1/2" ar500). But I was impressed with the damage that these little guys did to that plate.
I think someone with a mini lathe could do a better job of cutting the hole straight. I found the best way was to cut it quickly, then when I pressed in the rod of the same diameter as the drill bit I pushed it in just a fair further than the hole depth. They stuck pretty good in the bullet. Tested a couple lower velocity loads to make sure there were no issues, then loaded them up to about 3700-3800 fps if I recall correctly, could have been 3900, but pretty sure I didn't break 4k. It was surprisingly impressive.
You can get up to 1/4" tungsten rods from most welding supply stores for use as tig welding electrodes. I tried 3/32 and 1/8 inch rods. The larger were hard to drill properly and I probably ruined over half of the bullets I tried drilling. The 3/32 and 1/16 were easier but the 1/16 wasn't that effective. I bet a 1/4" rod in a 308 caliber projectile would be devastating.