Getting the diving software run on a small one chip computer is not the real problem (I can confirm that for example Subsurface compiles pretty much out of the box on both RasperryPi and C.H.I.P.. The challenging part is to come up with a box that can withstand the pressure while exposing the pressure sensor to the outside. Once you manage that, you can start worrying about the electronics and the programming.
If what you are really looking for is a small project involving a single chip computer and scuba diving you could help me with something that I have been trying to get to work for a while but due to lack of time have not finished: Create a small device that allows to read out non-bluetooth LE dive computers with a phone (in particular iOS): Use the RPi (or whatever) to actually talk to the computer over USB or serial or BT classic (as I said, that pretty much works out of the box using Subsurface) and then relaying that data via wifi to the phone (by creating an access point and acting as a subsurface cloud server).
All the bits are there, they just have to be tied together. If interested get in touch with me and I will provide you with further pointers to what has already been done.