All you had to do was start the easiest level of the quest - fight the 3 champs, exit out and go back in. The instructions state you retain the sling if you did not finish the level. You could repeat this numerous times to reach the objectives quickly, and without doing any arena. Then do the runs to completion on the highest level you were comfortable completing to get the best rewards for each run.Also FYI, for daily completion events, you could also run these just by going straight to the exit a couple of times and not using any sling.