Start a career/manager mode.
I chose Barcelona, it works best to choose a top team from Spain, England or Italy. It is possible with lower league teams, however it took me 3 seasons with Bradford City to be successful!
Then you must play or sim games until the January transfer window opens. You can only request funds during the transfer window, requesting at the start of the season is always declined by the board! They need to see more of you as a manager before giving you more money. When the January transfer window comes around you need to be in a good position in the boards eyes (High up the league table and still in the cups, however this just makes it more likely to happen)
Then to request additional funds you need to go to the Career Mode menu and go into the "Manager's Office" tab and then select "Request Funds"
When you are entering the parameters to request funds, request a low amount such as £100, then there are options to change your board expectations. Say you will win the league, win the cup and if in European competitions, say you will win this too. The achievement will pop.
However if you are playing normally in a career mode, you can normally request 2 million in the first season with realistic goals. To boost funds you can also buy a 'club takeover' from the EA Catalogue, then you get about £40 million I believe, but this is not for the achievement.
Happy cheevo hunting!