Found out how to access lambda logs from another answer
Is it possible to tail them? (manually pressing refresh is cumbersome)
Since you mentioned tail-ing, I'm expecting that you are comfortable with working on the terminal with CLI tools.
You can install awslogs locally and use it to tail Cloudwatch.
e.g.
$ awslogs get /aws/lambda/my-api-lambda ALL --watch --profile production
Aside from not needing to refresh anything anymore (that's what tail is for), I also like that you don't have to worry about jumping between different LogGroups (unlike in the CloudWatch console).