This achievement appears to be obtainable outside campaign mode, but it needs a slight workaround.
Unfortunately, campaign mode requires a new timetable to be setup every few days, so it is incredibly inefficient at increasing your bank balance. 'Mission or Survive' on the other hand can rack up profits very quickly as you can 'set and forget' the train timetable and leave your Xbox on overnight.
To unlock this achievement, I had a Mission or Survive (MOS) save with 500 days and $50m in the bank. I simply started a new campaign game, and them quickly loaded my MoS save and the achievement unlocked instantly.
It is isn't clear if it would unlock when hitting $35m within the save, or whether it needs to be 'loaded into'. The reason for this is that this achievement was unobtainable from the game's launch, so I have not been able to confirm. I will amend the solution if anyone can report otherwise.
This game has a number of poorly worded achievements, and where despite the conditions apparently being met, the achievement may not unlock. The above is by a distance, the quickest method, and by all accounts - and at the time of writing - only two of us have unlocked the achievement on TA, and both used this method.