Check this news link : timesofindia.indiatimes.com/city/goa/Dirty-Dudhsagar-A-beauty-disfigured/articleshow/15716709.cms
I believe the train that is mentioned here is this Amaravati Exp itself.
Some of the statements there say:
"The train halts at the small Dudhsagar station every Tuesday, Thursday, Friday and Sunday"
"The...
more... second tier above, along the railway track, is an unmanned area. It is accessible around the year by train, but visitors cannot scale down the hill to the pool due to the steep gradient."
Can someone confirm this that this train halts at Dudhsagar both towards Londa and towards Madgaon?