If you have an APM 2.5 / 2.6 and you get the Bad Gyro Health, it is highly probable that you have a blown 3.3v regulator on your board, this regulator is in charge of supplying power to the Gyroscope, that's why you will get this message.
If you have a multimeter please measure the voltage on the outer pins of the I2C port, if you get 3.3v then the regulator is fine, if you get any other voltage then it is a case of a damaged regulator.
You can get a better explanation of measuring the regulator by clicking here.
How these regulators have been burnt out?
How can we fix the regulator?
Option #1: If it's a new board (so that it's less likely you burned it out yourself) you could report the problem to the retailer that sold you the board and ask for an replacement. If it's 3DR it's called an "RMA".
Option #2: if you're handy with a soldering iron you can replace the regulator yourself. On the APM2.5.2 (and higher) boards it's not that difficult. On the APM2.5 it's far more difficult.
For APM2.5.2 : TPS79133DBVR
For APM 2.5: MIC5219-3.3YML TR
How can I stop it from happening again?
Do not connect any devices such as a radio receiver, MinimOSD, GPS, etc while the APM is powered especially while powered only through the USB cable.
Attaching a 100uF capacitor across any of the APM's radio input's 5V and GND pins will stop the regulator from being blown by plugging in a receiver video here!
There are very few reports of regulators being blown twice and no reports of it ever failing in flight.
1) Grab the APM and power it up via USB or Power Module but not both