Outputs on the Berry mixer are at audio Line Level, between consumer +10 and Pro +4.
This cannot be connected directly to microphone level inputs on a ham transceiver.
A resistive Y pad should be constructed and placed between the output line of the mixer and the input to mic jack.
Alternatively, wiring in a ~2.2K resistor in series with the hot of the audio output from either R or L output of mixer, then placing the outer terminals of a 10K pot across that to shield, taking the output to mic from the wiper can give you an adjustable level set, you want to set that such that the greater range of the Master Output fader on the mixer will not overdrive the mic input to the radio.
Be advised that these little Behringer mixers are not too good on the RF suppression, which can be problematic. Test on 20 meters to see if RF is getting into the thing, 20 being the most likely culprit in most cases. RF can be suppressed using a 1,000uH choke in series with the mic input positive in most cases, sometimes a ~100 - ~220pF capacitor across the mic capsule can do it, too. The choke is the preferred method, place as close to input of mixer (or physically inside the mixer) in series with the hot line of the mic.
The mic preamps in these things are balanced input, typically, wire as unbalanced to use standard two wire mics. You can find that info on the web.
Now that we are through all that, this is an excercise in bad audio, really, unless you can do on-air monitoring of your signal it is not advised at all for SSB communications. Most exceed the passband of the radio and create more on-air problems than any conceivable advantage by going through all of the necessary steps to achieve this one. You cannot put twenty-to-twenty audio down a 3KHz passband without problems. A good communications grade mic that matches your voice plus judicious use of the controls within the rig will smoke this solution every time, honest.