The following steps for linking a Metric with Amplitude works for any metric, included North Star Metric (NSM).

• Integrate your Product with your Amplitude account.

• Find the "Integrations" menu on the left sidebar.
• Click "Add Integration" on the Amplitude integration.

• Enter your Amplitude Project Keys and Secret.
• Check here for more details: https://segment.com/docs/destinations/amplitude/

• Click "Return to Metrics"

• Find the metric you want to connect with Amplitude and select it.
• Once on the metric page, scroll down and below the chart you will find a panel with all the metric measurements.
• On the top of that panel, you'll find some Action Buttons. 
• Select "Link Behavioral Data".

• Follow the steps on the page to link your metric with Amplitude.

• 1: Select Amplitude
• 2: Skipped if you're already connected with Amplitude.
• 3: Select the event you want to link to the metric.
• 4: Click "Measure Event" to preview the data.
• 5: Click "Link Data" to finish.

If everything went well, you should start seeing your metric measurements from Amplitude in the table below the chart.