The correct option is D has not yet completed
The underlined phrase "did not yet complete" sounds incorrect, because "did" does not refer to a continuous action whereas "yet" means 'till now'. It suggests a possibility of an action to continue.
Option A: 'Does' and 'complete' refer to the simple present tense. They describe an action that takes place on a daily basis, whereas 'yet' refers to an action that is expected to continue. Hence this structure is grammatically incorrect.
Option B: Similar to the underlined phrase, 'did' and 'yet' do not go with each other. Hence B is incorrect.
Option C: 'Is...completing' refers to a continuous tense whereas the action here (which has not taken place) is in the perfect tense. Hence C is incorrect.
Option D: 'Has not yet completed' refers to an action which has not taken place till the present, but is expected to take place in the near future. The auxiliary 'has' goes with the past participle 'completed' to refer to the present perfect tense. Hence D is the most suitable option. ('Has not completed' is in the present perfect tense.)