Try to install
libatk1.0-dev. That package contains header files for ATk. In Debian based systems, like Mint or Ubuntu, packages with different suffix have special meanings. Let's say libatk1.0 package. In Debian, it is splited to libatk1.0-0 libatk1.0-data libatk1.0-dev libatk1.0-dbg libatk1.0-doc.
If you just need ATK program(or other programs need it for package dependency), libatk1.0-0 is needed to install.
If we want to look up API documentation of ATK, libatk1.0-doc is needed, and we can look up its API manual in Devhelp.
libatk1.0-dbg package is almost never needed by common users. It's used for debugging ATK program.
libatk1.0-dev contains C header files. If a program is complied now, and it calls ATK's API, it needs atk's header files(like your problow). If you want to see where the headers files are installed, use this command:
dpkg -L libatk1.0-dev.