First it is required that all home owners control the drainage of their water as not to allow it to travel to the neighbors. You might be able to work with your neighbor PEACEFULLY ( do not want to live near neighbors who hate you) to correct this problem.
No retaining wall will stand with out perpendicular structural stabilizing. I have installed bulk heads on beaches and ponds. As well as retaining walls between poorly graded neighboring yards. Not even the smallest of these will stand up for long with pressure from only one side with out stabilizers. In fact it is dangerous to make one without them as a sudden collapse can cause injury or death.
What this means is that Long anchoring rods will need to pass through the wall and into the back filled dirt for several feet. They can be treated wood, galvanized rods or anything that will withstand contact and burying in dirt.
The best ones I have seen constructed are of old railroad ties. ever so often one is turned out to be burried in the dirt back fill. This is done on the 3rd and 2nd to last rows. More so if the wall is higher than a few feet.
Others creative ideas are creating a CURVED wall. Using Old tires ramed with dirt and filled with flowers tiered they can look quite pleasing when done. In fact an EARTH SHIP is built in such this manner.
There are the new terrace landscape bricks that can be used if employing this curvy method. As long as you do not need to go too hi as the cost can be quite hi.
The last idea I think would serve you well and far cheaper than them all is cutting a proper swell between the 2 properties on the property line. As long as there are no major obstructions this should not be hard. I can meander around anything you see fit and hopefully you 2 can find a compromise.