Tankers appear to occupy a logistics support role in the naval formations encountered throughout Armored Core: For Answer. They have no offensive capabilities and their armor is typically defeated by roughly two shots from a rifle. They are more than likely carrying volatile fuels or ammunition, as they explode dangerously when destroyed, damaging the player NEXT and destroying most surrounding Normals and other ships.
By targeting Tankers, the player is able to conserve both time and ammunition, as the resultant explosion will likely destroy most surrounding targets. This is particularly useful in the mission Attack on Naval Port of Mimir where these explosive ships are commonplace.
A word of advice would be to avoid using blades, as it result in you being caught in the explosion.