The challenge achievements can all be completed in one run through and are all relatively simple and shouldn't take that long.
From the main menu select
"Challenge". Select your region you prefer to play in and name your park, importantly change the diffuculty to
EASY. The diffuclty doesn't affect the achievements it just makes your game a lot harder!
When you're in the game you'll start with limited supplies. Don't blow your money straight away, make a few cheaper rides and work your way up.
Every few minutes a new challenge will appear in the top left hand corner. Simply complete one of those to nab the achievement. If the challenge seems too difficult you can scrap it and wait for a new one to come in!
Depending on how much effort you put into your park it will roughly take an hour or two to complete the ten needed!