'I went to do my best' doesn't really make sense and I can't think of an example where an english person would say that. 'Went' means to go somewhere so I think you mean the word 'want' so you could say ' I want to do my best' or example 'I want to get 100% on this exam' but in this case I would use 'I will try to do my best' as that would make the most sense to me.