At the start, deploy Link and Impa to defend the two main gates. Impa's speed and clone ability make her excellent for clearing large groups of enemies quickly. Use her Y-Y-Y-X combo to generate symbols, then press X again to consume them for a powerful area-of-effect attack. Link can handle the tougher Moblins and Lizalfos with his strong single-target damage.
Keep an eye on the gate's health bars on the UI. If a gate is taking too much damage, quickly switch to the character defending it and clear out the enemies. You'll face several waves of enemies, including Fire Lizalfos and Ice Lizalfos. Exploit their elemental weaknesses if possible (e.g., ice attacks for Fire Lizalfos, fire for Ice Lizalfos). use your special attacks when surrounded.