The good folks over at RCGroups.com have already reverse engineered the firmware for the Eachine H8 mini (and many other quads as well). We followed these step-by-step instructions.

The kind manufacturers have even labeled the pads that we need to solder our programmer to. 

Unfortunately the labels are wrong. DAT and CLK are switched. This is all documented at the above link. After a bit of downloading, installing and reading parts of the files in the GitHub repository we were able to connect and reprogram the Eachine H8 mini.

This we did in only a few hours. Don't be discouraged if this sort of thing takes you more time, more tries and results in bonking your head against the table. We have all done that. The reason that this was so quick was of all the hard work of silver13 and many others over at RCGroups.com.

To convince ourselves that we had reprogrammed the Eachine we inserted a command called failloop() at the beginning of the firmware. failloop() is an infinite loop that does nothing but blink the LEDs.