edit - this seems to be currently unobtainable,
To unlock 'On My Own' you must wait for EA to put up a "Be A Pro" challenge.
This can be found from Kick-Off, then Highlights of the Week.
Once there, select Be A Pro challenge. If you just want the win, pick amateur difficulty.
It will put you in the shoes of one player, and you need to meet the requirements.
For example, for mine, you play as Pedro and need to score a hat trick vs Getafe in the remaining 75 minutes.
Once you finish the match, the achievement will pop.