MongoDB insert performance rapidly dropping
The MMS monitoring graphs show that your disk basically can't keep up with the volume of data you are trying to persist to disk.  The flush average is hitting over 100 seconds.  Since MongoDB flushes data to disk every 60 seconds by default, that means that successive queues are queuing up and then impacting everything else.  Basically you need more IO to sustain the write workload you are performing, likely an SSD, for that kind of sustained writing.  

You can try throttling things by using different write concerns interspersed to get a more consistent throughput without completely overwhelming the system (check out j:true and a concern greater than 1 if you are running a replica set).