There is a great spot I found with 3 beggars that you can take advantage of and get this achv fairly quickly.
In Acre all the way west of the map on the border of the Poor District and Rich District. Start where Altair is on my map (location of 1st beggar) continue south at the border line is beggar #2 continue further south on the map until you see the break between buildings, head down the stairs and beggar #3 is right there.
Head back to beggar #1 and repeat until you get the achv.
*Note: As other guides have stated, you must do this to the women beggars not the drunk/mentally ill citizens.
Hope this helps.