You can currently either access the cron logs through the dashboard, or use the shell window as way to get access to the container. Though, for what you are looking for, you might be interested in using our upcoming API, which we are expecting within a couple of months.
Can you link to the API you mentioned here?
This is post is on a 3 year old topic, the API probably referred to here is our REST API at https://render.com/docs/api
John B
Render Support, UTC 