You have a few options:

1. Take the test in Berlin. The test report has to be within 72 hours prior to the flights in order to be valid to fly from Mumbai to Goa.
2. Take the express test in Mumbai. Results take 13 minutes. That being said, there might be a queue or some other waiting time before you're able to take the test.
3. Take the RT-PCR test in Mumbai. Standard test, takes 24 to 48 hours for results.

Here's some information about the express test (emphasis mine):

• Chhatrapati Shivaji Maharaj International Airport, Mumbai has introduced a new round-the-clock COVID-19 express test centre
• Chhatrapati Shivaji Maharaj International Airport is the first airport in the country to introduce the express test called ID NOW by Abbott Laboratories
• Here, flyers can receive their test results in 13 minutes
• The test, priced at Rs. 4,500 per test, is pricier than the RT-PCR test, however, it is quick and provides accurate diagnosis
• The testing facility is in Terminal 2, Level 2, exit Gate B
• Flyers arriving in Mumbai from International destinations as well having connecting flights can avail this test
• Flyers who test negative will be allowed to carry on with their travel, however, people who test positive will be sent to the respective institutional quarantine centres in Mumbai

More on test requirements (emphasis mine):

If you’re travelling to Maharashtra from Gujarat, Delhi – NCR, Goa, Rajasthan and Kerala, you will need a negative RT-PCR test.

This is applicable to all travellers irrespective of whether they are travelling by flights or trains.

For air passengers, the test report has to be within 72 hours prior to the flights.

Covid-19 Testing facility at Mumbai airport

Mumbai airport authorities started the ‘Abbott ‘ID Now’ Covid-19 test for flyers on December 15. Flyers need to pay Rs 4,500 for the express test. Since its launch on December 15, Chhatrapati Shivaji Maharaj International Airport (CSMIA) has witnessed an average of 30-35 such tests per day.

RT-PCR testing facility for domestic, international passengers at Mumbai Airport

Apart from the express Covid-19 test, flyers can also opt for a regular RT-PCR test. There is an RT-PCR Covid-19 testing facility available for all domestic arriving and departing passengers at Level 10 – Departures Area. Test results will take up to 24-48 hours for arriving passengers and 8 to 10 hours for departing passengers and will be sent via email. Flyers need to show Valid ID proof to avail of such test which costs Rs 850. Passengers who test negative will be allowed to continue their journey and flyers who test positive will be sent for institutional quarantine in Mumbai, CSMIA guidelines on its website read. All International arriving passengers can avail of the RT-PCR test for Covid -19 at the T2 Arrivals Lounge Area. Test results will take up to 8-10 hours and will be sent via email and flyers need to pay Rs 850 for the test, Mumbai airport authority said.

Personally I suggest you to take the test in Berlin, the day before departure. This would give you 72 hours to reach your destination, without having to take other tests.