Yes, this can be a DIY repair depending on your abilities. Here is some info:
This is a good discussion of the issue. Be sure that you are convinced that the gauge is ok before replacing the sending unit in the gas tank.
https://www.renntech.org/forums/topic/39099-fuel-gauge-stuck-on-full/
This is how to remove the fuel sending unit/fuel pump:
Porsche Boxster Fuel Pump Replacement - 986 / 987 (1997-08) - Pelican Parts Technical Article
This is a diagram of the system. The level sending unit is #5. The pump attaches to it (#4). I included the parts numbers for your reference.
And here is a link to buy the part from our Forum sponsor, Pelican Parts:
http://www.pelicanparts.com/catalog/SuperCat/1050/POR_1050_FULFUL_pg2.htm#item3