An RBI refers to the scores or runs recieved by the team as a result of the player at bat succesfully hitting the ball. A single player must earn ten of these. These also include if the player at bat scores themselves. The achievement will not pop until the end of the game, so you'll have to keep track of who's batting and scoring. I had to do this in a 7 inning game, but I also super suck at sports games so you might be able to do it in 5.
Just a general tip, use contact swings to load up the bases until you have a heavy hitter. Then swing for the fences and hope for a homerun.
This is of cousre unless you have a turbo, use that for a grand slam. As long as your marked batter(s) (I did two at once just to be safe) are hitting getting 2-3 runs at bat per inning you should be alright.