DD has 8 teeth and I've just noticed that the bottom ones appear have tartar along the gum line

I have been brushing her teeth at bedtime with a baby toothbrush since about 8 months but I guess it's not been effective enough... if I'm honest it's been a few swipes from me and then giving her the brush to chew.
But if I try to brush "properly" (ie the way I would brush my own teeth) she will yell and fight.
What does everyone do? Do I need to forcibly brush even if she cries? Help!