With the Capture feature
Genymotion Device image (PaaS) includes a Capture feature. Please refer to Genymotion Device image (PaaS) user guide: Capture feature.
With ADB
Connect your instance to ADB. Use the adb shell screenrecord command (see https://adbshell.com/commands/adb-shell-screenrecord).
With HTTP API
From your instance web display, go to API reference (see Genymotion HTTP API). Use the API called shell. This API allows passing commands to execute on the device. Use the command screenrecord [options] /sdcard/record.mp4. This will record your screen in a record.mp4 file in /sdcard which can be retrieved with the files HTTP API.
Note
The default recording time limit is 180 seconds. This can be changed with --time-limit option. Maximum value is 86400 (24 hours).