It is a common belief that the government must ensure the well-being of the environment.

>>> GRAMMATICALLY CORRECT~!^^ GOOD JOB!

 However, there is a more persuasive argument that the residents are responsible for the environment because how to use environmental resources plays a crucial role in conserving ecosystems.

REVISED:  However, there is a more persuasive argument that the residents are responsible for the environment because the way environmental resources are used plays a crucial role in conserving ecosystems.

Original: "because how to use environmental resources plays a crucial role"

Correction: "because the way environmental resources are used plays a crucial role"

Reason: The phrase was grammatically awkward.

On the one hand, some environment needs the government’s attention because of the extent of the nature.

REVISED: On the one hand, some aspects of the environment need the government’s attention because of the extent of the nature.

"some environment needs the government’s attention" → should be "some aspects of the environment need the government’s attention"

 For example, in the case of the mountain, prevention of forest fire and protection of wild animals, trees and other nature are require significant exertion.

REVISED:  For example, in the case of the mountain, prevention of forest fire and protection of wild animals, trees and other nature require significant exertion.

are require significant exertion → require significant effort (omit 'are')

 They can’t be managed by just individual’s effort.

REVISED: They can’t be managed by individual efforts alone.

 In addition, the government must suggest guidelines for people not to harm any nature resources. 

REVISED:  In addition,  the government must establish guidelines to prevent harm to natural resources.

Without restrictions, nature will be led to serious consequences in the short future due to limited resources.

REVISED: Without restrictions, nature will face serious consequences in the near future due to limited resources.

be led to” → changed to “face” (more natural verb choice).

in the short future” → should be “in the near future” (standard expression).

On the other hand, I support the idea that people who use the environment have essential roles in managing. 

REVISED: On the other hand, I support the idea that people who use the environment play an essential role in managing it.

Added “it” at the end to clarify what is being managed.

In fact, it is impossible to preserve ecosystem without individual’s attention to it. 

REVISED: In fact, it is impossible to preserve the ecosystem without individuals’ attention.

“individual’s attention” → should be plural possessive “individuals’ attention”.

To be specific, water pollution is getting critical nowadays.

REVISED: To be specific, water pollution has become a critical issue nowadays.

“is getting critical” → awkward phrasing → changed to “has become a critical issue.”

 This is mainly due to the lack of awareness in environmental contamination from people who go on trips to sea.

REVISED: This is mainly due to a lack of awareness about environmental contamination among people who go on trips to the sea.

“the lack” → “a lack” is better when introducing the idea for the first time.

“awareness in” → should be “awareness about” (correct preposition).

“to sea” → should be “to the sea” (missing article).

“from people” → changed to “among people” (preposition agreement with "awareness").

 They usually tend to leave their garbage in the beaches.

REVISED: They often leave their garbage on the beaches.

 Of course, these trashes have a negative impact on the nature.

REVISED: Of course, this trash has a negative impact on nature.

“trashes” → incorrect (uncountable noun) → should be “trash.”

on the nature” → should be “on nature” (no article needed).

Actually, the best way to preserve the environment is to let people obey the rules that don’t damage on the nature.

REVISED: Actually, the best way to preserve the environment is to encourage people to follow rules that do not harm nature.

“let people obey the rules” → awkward; improved with “encourage people to follow rules.”

“don’t damage on the nature” → grammatically wrong → correct phrase is “do not harm nature.”

To sum up, while it is apparent that the government should take care of the environment, it is undeniable that individuals must play vital roles in conserving the nature.