Front derailleur is hard to shift into the big ring. Where to start?
First off, of course, lubricate the cables and assure that the derailers are properly adjusted.

After that, make sure you're not cross-chaining too much when shifting up -- you should have your rear near the outer cog before up-shifting the front, so that the angle of the chain isn't fighting you.  Also, understand that you must let up a hair on the cranks when up-shifting the front -- don't do it under full load.

But if not that then likely the rings are worn out.  Even if the chain and rings gauge out OK (did you check them??) the ramps on the side of the big ring may be worn to the point that they're no longer effective.