In order to clarify what exactly counts as the objective for a mission/area, here is a list of every mission in the game and what counts as the objective:

Westside Hotel - Collect 25 Metal Head Gems.

Construction Site 1 - Complete the 4 crane fights.

Breeze Valley 1 - Spray all the plants and kill the queen.

Brewery - Complete the minigame to lower the water.

Transit System - Complete the train chase and kill the Hive Queen.

Strip Mine 1 - Collect all 8 Eco Crystals.

Breeze Valley 2 - Spray all 8 bugs then kill all 3 queens.

Tanker 1 - Collect 30 Metal Head Gems and Complete the minigame at the end.

Distillery - Collect 40 Metal Head Gems.

Fish Cannery - Collect 40 Metal Head Gems.

Emerald Isle 1 - Take down the large bug.

Construction Site 2 - Destroy all the termite mounds.

Strip Mine 2 - Destroy all 30 nests then kill the Hive Queen.

Lumber Mill - Kill all 7 of the large bugs.

Emerald Isle 2 - Take down the large bug again.

Tanker 2 - Beat the timer to the end of the level.

Palace - No specific objective, continue through to Prison.

Prison - Complete the minigame to open the door to the final boss.