aakk9999 - 3:40 am on Dec 24, 2013 (gmt 0)
It looks like your first drop has been caused by Penguin 1.0. But looking at the chart prior to April, it seems that the traffic started to raise somewhere in the second half of March. Has the site a seasonal trend? If not, what happened in the second half of March that caused the site to gain traffic fairly sharply? Because the drop in April 24th seems to reduce the traffic to where it was at the beginning of March.
As for the latest drop (October and December 2013) - do you have Google Webmaster Tools account? If so, could you do the Search Query chart showing impressions that would cover period from the last week of September up to now? (There is no need to see the numbers on the Y coordinate of the chart, the chart line with dates below is enough).