Skip the over-priced solid copper stuff (for now), if you don't like spending much on ammo. Although the selection is a little more limited in 24 caliber than, say, 30 caliber, there are still a few bullets out there that can do the job at high velocity.
Try a tougher bullet. The 100 gr PSP Core-Lokt is simply traveling too fast, when it impacts at short range. That load was designed for the bullet to shed some velocity (250-300 fps, or more), before impact.
Although I have a great deal of respect for the Remington Core-Lokt, overall, and have been very impressed with its performance in .270 Winchester (130 gr), .30-30 (150 gr), and .30-06 (180 gr), some versions are a bit sub-par. The most notable, in my opinion, are the 100 gr version you'll find in .243 Winchester and the 165 gr version in .30-06. They tend to explode at close range, and often do the same if they strike bone at nearly any velocity.
(In my experience, the 100 gr bullets loaded in Federal's .243 Win Power-Shok and Fusion ammunition is just as prone to explode, as well - even at velocities seen beyond 400 yards.)
If you want to stick with Remington ammunition, I would suggest you try (in this order):
Remington Premier 100 gr Core-Lokt Ultra-Bonded
Remington Premier 90 gr Swift Scirocco II (great bullet)
Remington Premier 80 gr "Copper Solid Tipped Boat Tail" (Barnes TTSX)
If you're willing to try another brand, my suggestions would be:
Winchester Supreme 95 gr Ballistic Silvertip
Federal Premium 95 gr Nosler Ballistic Tip
Federal Premium 100 gr Noslern Partition
Federal Premium 85 gr Barnes TSX
Hornady Superformance 80 gr GMX
Nosler Trophy Grade 85 gr Partition