It is not clear what pangaga is trying to save. One possibility is : "I do not expect any difficulties with this task", which means "I do not think I shall encounter any problems." We rarely, if ever, use "I have no difficulties..." as a statement. I can't think of a situation where we might use it. I suppose if asked, "Do you have any financial difficulties?", we might give "I don't have difficulties" as an elliptical defiant answer. Another possibility is: "I had no difficulty in completing this task." Another possibility is: "I don't have a problem with doing this on my own", which means "I am willing to do it without help from others." Well, we don't know what pangaga wishes to say.

Can we remove the phrase "with my efforts"? I think the sentence will look (or sound) better without it. I think it's better to be like this, "I had no difficulties in finishing this task."

I don't think any native speakers would write either of the sentences.