The correct Passive form of the given sentence is:

☀ Let this task be completed as soon as possible.

So, the correct passive form is: "Let this task be completed as soon as possible."

The other options and their explanations:

☀ Let this task should be finished as soon as possible.

• This option is not grammatically correct. In the passive construction with "Let," the auxiliary verb "be" is used without the modal verb "should."

☀ Let this task completed as soon as possible.

• This option is not grammatically correct. It lacks the auxiliary verb "be" and uses "completed" as a bare past participle without a linking verb.

☀ Let this task be complete as soon as possible.

• This option is not grammatically correct. The correct form should be "be completed," not "be complete," to form the passive voice correctly.