Before they went under, A-Square made a "Lion Load" that was a thinly jacketed soft and not bonded. I have never personally used it, but it had a good reputation as a first shot cat bullet. I would think an ordinary Remington Core Lokt or Federal Hot Core soft point would work well for the first shot on a cat in any sensible caliber, though I would choose (based on my personal experiences) a Partition over either.

Again, for followups, a heavy double is just the ticket. In India, during the era of the Shikari, the classic tiger rifle was a double (they shot them from the backs of elephants). If you want to see a great tiger hunting movie, watch "Harry Black and the Tiger" with Stewart Granger (if you can find a copy). Read the books that Jim Corbett wrote as well. He was the ne plus ultra of problem tiger and leopard hunters in India.

I would dearly love to hunt tiger, but am just not willing to go to prison to do it. Read the Lacey Act for further details.