Upgrade your Siege Archers to at least lvl 3, so they have the range to kill Goblin Alchemists to end this stage. Elven Hunters won't clear them as effectively (will start being distracted by Orcs/Enemy Wall after a while) in my experience.
Start with 2 Bannermen, then Wood Elf Warrior. You'll need magical attack to clear their ground units for this stage. Don't build too much ground units as they will be nuked (literally) as they push past half-battlefield and enter Goblin Alchemists' range. Max your bannermen while holding off their offense with Elven Archers and a few ground units. Start building Siege Archers once you take control of the battlefield, and push down their base before the stage grows too hard.
If you are confident with your Ranged Weapon Skill, you can take a Ranged Weapon to help clear their wall units, maybe even backdoor their base if you somehow got stalled by strengthened enemies.
For the Achievement (finish this wave without building any unit):[]
It's hard to eliminate enemy units all by yourself, since they include both Goblin Mad Docs (immune to physical attacks) and Goblin Shamans (immune to magical attacks). So the easy way should be knocking down their base asap, while ignoring enemy units through long-duration AoE stuns (e.g. Retribution) or hero invulnerability. Besides, stack as many damage with rune/armor/shield as you can, and take a fast-attacking weapon. The Siege Hero research and skills such as Tremor Smash (extra damage to buildings) will also help a lot.
Take down the right side wall then directly rush the base tower, ignore their gate wall. A small tip is positioning behind their base tower and use it to block Goblin Shamans' ranged attack.