[PhasmaFelis]

I'm not an expert, but after some Googling, I think the bullet they're using there consists of a steel core inside a lead envelope inside a copper or copper-nickel jacket. So, at a guess, you'd want to replace the steel with something much harder and/or denser. Tungsten, maybe? I dunno. Depleted uranium would probably do it; I've never heard of it being used in anti-personnel rounds, but in cannon sizes it pokes holes in tanks quite nicely.

[hga]

Indeed. The AP M2 round is the standard for National Institute of Justice (NIJ) Level IV rifle plate armor, but to the best I've been able to determine it's not a "serious" AP round, rather, it has a pill of relatively soft steel inside the normal lead and was developed in the run up to our involvement in WWII as much for the lower cost as the increased penetration. The latter of which was appreciated towards the end of WWII when I've read it became ubiquitous, and for example in city fighting one or more 20 round BAR magazines of this were used to knock holes in masonry walls between buildings.

It was probably made the NIJ standard because it's the only somewhat common AP ammo a US cop is likely to go against on the street, as noted by extrapickles the serious AP ammo is a lot more expensive, and I'll add not really legal any more since there are some pistols that'll fire it.

Notably, ESAPI military equivalent plates also aren't certified to stop anything more serious than AP M2, and I assume again for the same reason, there is or was a lot of surplus AP M2 ammo out there at one time. In the US civilian marketplace it's pretty much dried up as I understand it, e.g. see the few hits this GunBroker.com search finds and the prices: http://www.gunbroker.com/Ammunition/BI.aspx?Keywords=ap+m2 and I can't find any demilled bullets there or with a couple of minutes of Google time, whereas they were commonly available not too many years ago, certainly within the last decade.

[extrapickles]

There are several rounds the military uses for small arms. 50 BMG and 5.56 NATO both have tungsten versions, though they are expensive, and hard for non-military to buy (when found, $50/rnd). Even the military does not normally issue them due to the cost, which is ~2-10x of a standard lead+steel round.