That's a tough one, there really isn't much you can do. I assume the wall runs along the property line, in which case both parties will have to sign off on the wall as it will be located on both properties. You could say that if they don't pay for half of it then you will have to put it on your side of the property line, but that's not terribly beneficial for either party. Depending on the type of wall, you could leave their side unfinished and save a little money.
Just a few things to note regarding contractors. There are some very good contractors out there and you may have a great deal but it is important to remember that construction prices really don't vary that much. I am a licensed C27 landscape contractor and have also been in residential landscape architecture for over 10 years now and I can tell you that if you are really comparing apples to apples with contractors the price might only vary by 10% - 15% or so. When you start seeing these large discounts, like 40% - 50% off another competitors price, that is a huge red flag. The cost of the materials alone on the job normally will run around 25% - 35% (and is the same for all contractors), which of course varies for each project. Labor on a job will usually run another 30% - 40%, and believe me, everyone pays about the same for their guys, this doesn't vary greatly. Then a contractor may spend another 10% - 20% on marketing, overhead, workers comp, general liability insurance, bonding and so on. The remaining portion is profit, which contractor aren't really going after these days. The only way for a contractor to get the price down significantly is to reduce the quality of the materials they purchase, such as flagstone, irrigation parts, lights, and plant material, but of course everyone will say they have a friend that gets them a special price. A real bad contractor may also not install re-bar in the concrete, pour the footings smaller on walls, not compact the base correctly, shortcut the lighting by using a "daisychain" technique and a million other unethical installation tricks. Also, they may go in with the lowest price, and deliberately leave things vague or off the contract so they can come back later and change order you at twice the price knowing you can't go anywhere at that time. All of these reasons are why you want to hire a professional Landscape Architect with construction experience to oversee the project, review your bids, help find a quality contractor, value engineer your project to stay on budget, and complete a thorough set of plans which the contractor is legally obligated to follow. Never have the contractor design the project he is going to build, this is usually a very bad idea and may cost you in the long run. Its not to say all contractors are bad, there are some great ones out there, we work with them, but, do your homework, and hire a professional landscape architect to help you out, the design fees will be nothing compared to what you can save. If you would like to view some interesting blog posts about the industry, and view some of our work, visit our website at www.studioh-inc.com . We are always more than happy to answer any questions you may have.