Can you please explain or sketch your planned layout of parts? At the moment your original question is very opaque, since it appears to be asking how to connect a four conductor tip/ring/ring/shield connecter to the audio board, but your second post shows a nothing with that would need that -
in which case it might just be as simple as running from your out+ and out- to the line in left/right and gnd pins on the audio board Edit - do not do this - if that board is what it looks like on the sparkfun site it will blow things up - see note at end
This will most likely not work that well due to input impedance differences
https://en.wikipedia.org/wiki/Input_impedance
and because that preamp looks like it is balanced and the audio board is unbalanced
https://en.wikipedia.org/wiki/Balanced_line
Can I suggest backing things up a bit and that your actual question is probably how to connect the Hydrophone to the audioboard? Depending on the Hydrophone and what you need quality wise using the audio board mic inputs and the inbuilt preamp may be all you need to get close enough quick enough. Working that out means knowing more about the hydrophone and what sort it is and what form it's output takes.
Edit - if that sparkfun board is
https://www.sparkfun.com/products/11044 that is not a a high quality audio/instrument preamp suitable for boosting small signals from hydrophones up to usable levels. It is a amp intended to boost line level audio to drive a speaker using a class D Amp
https://en.wikipedia.org/wiki/Class-D_amplifier generally not what you want in any high quality audio path. It will work if you are after a low fidelity output to drive a small to medium speaker on the output end of the Audio board though.