Grand Duchess Olga Nikolaevna, eldest daughter of Tsar Nicholas II, the last autocratic ruler of Russia, nursed wounded soldiers during World War I.
A. Grand Duchess Olga Nikolaevna, eldest daughter of Tsar Nicholas II, the last autocratic ruler of Russia, nursed wounded soldiers during World War I.
[correct - the modifiers are correctly spelled out and no obvious issues]
B. Grand Duchess Olga Nikolaevna, a nurse of wounded soldiers during World War I, the eldest daughter of Tsar Nicholas II, who was the last autocratic ruler of Russia.
[incorrect - this changes the meaning (which is the least of this options problem)]
C. The eldest daughter of Tsar Nicholas II, Grand Duchess Olga Nikolaevna, the last autocratic ruler of Russia, nursed wounded soldiers during World War I.
[incorrect - the eldest daughter here is the last autocratic ruler - that's wrong]
D. During World War I, the eldest daughter of Tsar Nicholas II, the last autocratic ruler of Russia, Grand Duchess Olga Nikolaevna, nursed wounded soldiers.
[Incorrect - same as above]
E. Nursing wounded soldiers during World War I, Grand Duchess Olga Nikolaevna, the eldest daughter of the last autocratic ruler of Russia, Tsar Nicholas II.
[Incorrect - this is not even a sentence and is a run on clause]