Moose- I'm sure this could be done with a 270, but this animal has some big bones. I would think 7mm mag, wsm or larger, probably a 30 cal would be sufficient.

Grizzly and polar bears- This is where the saying "size matters" comes to mind. Certainly no personal expierience, but I would think 338 or bigger. I wouldnt attempt these with a 270 thats for sure!

Lions- A 270 maybe big enough, no clue. It would be my personal opion that if you could afford the cost of a hunt like this, then you can afford a new rifle to hunt them with!

Tigers- I belive tigers are endangered everywhere they exsist, so no worries there. If youcan hunt them somewhere then this would the same thing as lions.