
Deborah P. answered 06/23/19
English, Reading, Writing Coach
Yes, my hardest is a direct object in the sentence "I will try my hardest".
According to The English Language Guide, direct object answers the question "What?" or "Who?".
For example, in your sentence the what question is “What will you try?” The answer is “I will try my hardest.” You are correct in asking further questions, and if you’ve checked The Cambridge Grammar of the English Language publication, I’m sure you discovered there is a lot of debate about that identical sentence.