Seems to me you've completed the first battle. At the place where you select the battle, just select the next one. Though it also appears to me the battles are shorter (in number of missions) in TIE Fighter. Which group of missions did you complete? Combat Chamber?
Note: Battle 6, Mission 3 in TIE95 is known to cause a lockup (or crash to desktop in Win2K/XP) and needs to be patched. Look here
for it (the file is linked to the "Download Now!" text at the bottom of the page...follow the instructions on the page).