It's not even worth it!. You DON'T NEED a powered microphone for an action camera.
The 3350 is driven by popularity and comes from a community not related to the "action camera" scene. Somebody saw the recommendation from a video forum that is focused at DSLR's and those recommendations are not too relevant for our action cameras.
I get it, it's hard to choose a microphone and the Drift or gopro mic is expensive but the 3350 is not the "one size fits all" mic you all should be getting.
Using a powered mic means making an internal part of the camera redundant, it's the microphone pre-amplifier. Your camera has one built-in and you're attaching another one between the mic. That's the part in the mic that requires power from the coin battery. It's redundant and not needed and you're getting into a world of trouble to make that mic-preamp work, messing with batteries, power switch, not knowing when the mic is working since the camera doesn't have an audio monitor or audio level meter.
Also, the ATR-3350 is a Lapel mic. Its a mic made to be held far away from the mouth, out of view, to capture voice at a certain distance and has a long cable to make it run from the actor to the camera or recording device.
The amplifier inside the mic makes sense for that application because it needs to amplify the voice because it's not close to the mouth and also, the signal needs to overcome the noise that such a long run of cable may catch. With a low-level signal, the noise will be high enough to get mixed with the voice, making the recording useless. The solution is to amplify the voice signal as soon as it gets to the mic, then run the amplified audio through the cable and the noise becomes insignificant.
I should make all this into a new thread.