"I achieved some great results." means that you had a number of results that were amazing among all of the results, but maybe not all of the results were amazing. I don't think it has a negative connotation, particularly if you're talking about something that has a lot of variability beyond your control, like for example, training aggressive dogs to make them less dangerous.
"I achieved great results." has the sense of "I used this tool in the circumstances that called for it, and it consistently did well."
In general, when we say "some X" instead of just "X", we are qualifying our statement to mean "maybe not every X/all of X". That's not always true though. For example, "My husband brought me {some} flowers." The "some" is optional and its inclusion has little effect on the meaning of the sentence. On the other hand, if I omit "some" from "I think {some} people like being angry." I change the inferred meaning to "I think (all people in general) like being angry."