There's some things you can do without removing the panel cover.
Sometimes just pushing slightly on a failed outlet brings the power back. If so, you've found your loose connection.
Assuming only one of the two connections (the hot wire, which should be the short outlet slot) is bad, run a 7-1/2w test lamp from a known good ground to each short slot of each failed outlet.
If you find one of the failed outlets that has an energized hot wire, turn breakers on and off until this outlet loses power.
Now, check what other outlets have lost power.
Now you have identified all the outlets on that breaker and with that breaker off you can use an ohmmeter to check where the bad connection is.
Checking the neutral wire requires the test lamp to go from a known good 120v source, but it's otherwise the same principle.
For those outlets that still work, if you have a voltmeter there is a way to check connection integrity all the way back to the power pole without removing any covers.