Also, consult your favorite local tooling rep. There are some amazing taps out there for this material.
You are looking for additional relief in the flute compared to a 'regular' tap. You WILL pay extra for taps specific to this material but the overall reduction in cost per threaded hole is significant.
Not to mention the reduction in level of frustration........
We do machining of 6Al4V titanium and use EM-TI taps from Greenfield.
Tapping titanium presents some unique problems compared to other materials. It has a tendency to spring back because of its extreme elastic memory. I believe the EM-TI taps have extra back taper and radial clearance to help with the spring back effect. Because the tap has all this built in clearance, it will be alsmost impossible to use it as a hand tap because of lack of radial support compared to what a hand tap has. The tap I have mentioned should be used on a rigid machine with synchronous tapping ability. We run our taps around 6-10 SFM to determine the correct RPM. You may also want to try and increase the taps H limit. For example, if you are tapping 2B threads with a 3/8-24 tap, the H limit would be H3. You could go with a H4 or H5 tap to help with the springback. Each increment of H limit cuts .0005" bigger or smaller depending on which direction you go. Make sure the drill you are using, prior to tapping, is making a round hole. This is crtical to the taps success. Make sure you are using a lubricant that has high lubricity. We tap on a CNC machining center and run our water to coolant ratio around 14%. Greenfield is a Kennametal company so you may to try and start there to contact a tech guy.