She brought up three children single-handedly. (need to use past tense of bringing) She is bringing up three children single-handedly.(most common way) She is bringing three children up single-handedly.(you will hear this way but bringing up is the natural way) She has been bringing up three children single-handedly. you can also use the alternative word "raising" or "raised" for the past tense sentence,

She is bringing up 3 children single-handedly. ('bring up' should be together in this case, maybe not in others, like : 'She wants to bring them up right') :)