The first mission that Professor Briel is available for use is level 04. You can also her on the 'Fully Loaded' variant of any level, as early as level 01.
After you choose your game mode, scroll over to the right when selecting Command Team and choose Professor Briel. Then, just hold
during the level to fire her cannon. This cannon gives resources based on enemies hit.
Note on Professor Briel Availability
No AIs are available during mission 16.
As with all other achievements in this game, the achievement won't unlock until you beat the level.