One of the great things about the Retron 3 is that some of its individual components can be used exclusively of the others. Such is the case of the Nintendo-on-a-chip that Hyperkin uses in the Retron. This guide shows how you can separate the NOAC for use in a portable or mini-console.
To start, remove the NOAC (top-most board) from the rest of the Retron.
You can still run the NOAC from the Retron's AC adapter, but it would be more efficient to run the board from a 5V source. The 7805 regulator and capacitors on the bottom of the image manage the voltage coming in from the AC adapter. Since we're going to be using 5V instead, those three components can be removed. Likewise, the AC jack, S-video, and RCA jacks can be removed.
The NES controller ports are located elsewhere on the Retron, but fortunately the individual pins of each controller can be wired directly to the NOAC. I have given the pins the following arbitrary numbering. Pin 1 must be connected to ground and pin 5 connected to 5v.
The pinout from the bottom of the NOAC showing the relevant connections to voltage, ground, controller connections, and audio/video. P1/P2 represent player 1/player 2 controllers.
Once stripped of its larger components, this NOAC can be used to create a very small portable.