Spoilers ahead for the second district's route, its gates and its final boss.
The Construction Site opens after you defeat Hobo Dad. Follow the entrance road, wide street, narrow alley, unloading area, passage between unfinished buildings, main site and the Foreman's arena. Road markings and section names help you stay on course.
Opening the barriers
Progress depends on specific enemy groups. The route has 20 groups arranged in pairs across ten barriers. Defeat both groups tied to a barrier to open it. Defeating unrelated enemies elsewhere won't open that gate.
Groups can activate when they spot you, so a section may contain more than one active threat. Watch the current objective and look for remaining enemies. If a gate stays shut, check the nearby area and the section you just crossed.
In the alley, keep melee enemies from trapping you against a wall. Out in the open, check where the ranged attacks are coming from. Shops and supply crates along the route can help you prepare for the finale. You still need to finish the required group fights.
Fighting the miners
A miner winds up and marks the direction before throwing a pickaxe. Watch the windup and move out of the line of flight. A pickaxe already in the air keeps going after its owner dies, so keep moving even if your attack finishes the miner.
Think twice before running straight through a fresh group to reach a single ranged enemy. Clear room to move first, then close the distance when you can do so without getting surrounded. Adjust your targets to the enemies actually in your path.
The Drunk Foreman
After you've defeated all the groups, approach the final arena to trigger the boss. The entrance closes during the fight, so handle any shopping and healing before going in.
The Foreman uses a ground slam, a sweeping attack, a saw and a charge. As the fight goes on he becomes enraged, speeding up and shortening his windups. Leave more room to dodge than you needed at the start. Even when his health bar is nearly empty, watch the next attack before committing.
Victory awards 10 crystals and opens the Forest. Replaying and beating the district again also earns the crystal reward.