I'll assume you stick to factory ammo.
Winchester Fail Safes are indisputedly the toughest bullet out there today.
All the ammo makers have a Premium line with superb big game bullets. You could choose loads with Nosler Partitions, Barnes X, Bear Claws or one of the new bonded designs.
Shoot nothing lighter than 180 grains, and 200 would be better.
I'm not familiar with Remmy Accu-Tips, but from the name, I suspect they're more of a target bullet than a big game design. If so, they are NOT a good choice.
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