Though extremely effective against masses of units, the Demolisher lacks the health to withstand close combat conditions. Its firing range none the less demands that it get within a dangerous distance from its target in order to effectively pepper them with flak. Send in your Rock Heads first to draw fire and form a skirmish line before rolling these up immediately behind, and consider protecting the Demolisher with P-Shields. If this still isn't sufficient, Meteor Mobile Missile Launchers can soften up the enemy defensive positions.
While it might seem to help at first, the UEF Artillery Weapon Range research only affects structures, so this unit isn't suited to out-ranging enemies.
The Demolisher, when upgraded with Anti-Air, oddly does more damage than the Archanist Mobile Anti-Air Gun, at the cost of the projectiles not tracking quite as well.
The Demolisher's area-effect damage can be useful in late-game for stripping the shields off of enemy units, particularly when they are tightly packed.