I played Legendary solo. While in Cortana I used mostly the sword, brute shot and needler (and the occasional rockets etc.). Use the needles on the 'ranged form' flood (those that fire green spikes back - just a few needles will already kill them) and the sword or brute shot on those that attack you. Use also as many grenades as possible (ideally stickies). In case the flood swarms you make sure you don't stand still (run in circles). You have to retreat occasionally to deal with the flood. Also note that the flood explodes. So, when they are still concentrated in a small area a single grenade usually takes care of them all. Sometimes you have to move three weapons with you and drop them through holes to the next level. As someone already noted, patience is key here.