Edit: So this was true on season 1 and looks to change season by season:
So level 25 you will need to get 12,230 xp to be able to unlock it.
Challenges will be the quickest way to number.
There are a total of 7200xp given in weekly challenges
Daily there is 720 extra xp per day.
You need to qualify 8 times daily for one of the challenges and one qualify will give you 41xp for round one.
So daily expect minimum of 720+328=1048xp.
Also if you want to shell out the cash you can buy the 25 level skip and pay to win which was confirmed on the other solution.
Obviously I have ignored not qualifying as well as getting to higher rounds but at least you have a ball park of how to maximise your play time to get this achievement.
Edit. I just realised that the qualify for 8 rounds might change week by week so that part may or may not be correct depending on what your daily challenges are.
So because it will change so frequently (every 2-3 months) what I will say is this.
You can buy 25 levels to pop the achievement but to do it the free way challenges will get you there sooner. Challenge xp amounts change daily/weekly/seasonally so to give one solution is impossible.