Doing this the normal way is gonna be a hard one and will consume a lot of time
Here are the thing you gotta do to get this faster than the normal method
1.Go to match settings->Set no.of rounds to 1 instead of 2
2.Next go to Towers of time and select a tower with only one opponent(not the ko-op towers ,that ones are hard for individual players)
3.Fight the opponent and complete the tower in just one round.The tower resets completion rewards so don't back out from the tower
if you back out the tower will vanish and a another set will appear.
4.Continue completing the same tower as much as you want for a particular session.This will increase the no of completed towers in your kareer stats
When the tower count reaches 250,the achievement will popup
So that's the easier way to do it as of now

N.B: The no.of rounds configuration only works in single opponent towers
Also another tweak
Make your AI player finish the tower grinding, but i wont recommend using this AI setting .
Thanks for reading