I am not sure if my sentences are correct.

I'll be beginning to makstart doing the English tenses challenge on next month.

I have difficultystruggle with tenses.

This sounds more natural

Or, Ccould I say.

This is not a complete sentence. You would need to write a full question and end it with a question mark. Example: Or, could I say 'I'll begin to do the English tenses challenge next month'?

I'll begin to shardo the/participate in the English tenses challenge on next month.