After you kill Dr Steinman go to the balcony where they chuck grenades at you and grab one with telekinesis.

Then there will be a tunnel collapse, but don't let go of the bom,b then there will be an alternate route.

Take it, then a Big Daddy will be flung out of the window. After that happens keep going straight but dont drop the bomb.

Then if you angle it through the door there will be a video with that Splicer and the bomb will drop by itself killing the Splicer.

Then after the video Tenenbaum will still be standing on the balcony, shoot her and bring her down with telekinesis.