This is cumulative: You do not have to get one park to level 100I don't even know if that would be possible.
Anyway, every positive action you take in your park rewards you with
FAME. At certain preset amounts, your Fame Level increases by one - it's exactly the same as levelling up with experience points in an RPG.
Every game mode counts towards this achievement, including Sandbox mode with unlimited money. If you plan to get 100% out of this game, you will unlock this achievement some way through the campaign / challenges.
If you need to unlock it quickly, then go into Sandbox mode, set your admission price to free and start building everything you can. Once you've built every type of exhibit, start filling them with animals. Then build all the concession stands and the facilities.
One thing to note is that you unlock exhibits etc as you reach new fame levels, so as you build like crazy more things will become available. More expensive buildings and exhibits give more Fame, and it's the same for animals.
If things start to get slow after Fame Level 25, simply quit and restart Sandbox.
Some challenges will also reward you with Fame: Press
to see the list currently available. If it's something trivial like photographing a llama, do it!
Pulling the
on the picture of what you're about to build / adopt / hire will show you exactly how many Fame Points you'll get from it, as well as it's monthly upkeep should you not be playing Sandbox.
I unlocked this without rushing it after about eight hours of play time, but by speed building sandbox mode you could do it in a quarter of the time.
Have fun!
*Edit - Please comment on the downvote! Thank you.