If you dive right in and take on all the mobs at once, then it's impossible, but if you take your time, keep your distance and take on one mob at a time, then it's very doable, especially when you use the bow for the mobs walking at the speed of light when they idle for a moment.
It took me 5 minutes and 2 tries to complete it.
It still was fun though.
Random idea: it would be fun if you make a system with command blocks and the scoreboard system to tell you your maximum distance when you fail, and the time when you win.
Wow! Very Impressive. I enjoy hearing how you beat it and I really like your suggestion! Do you know a way I can do the maximum distance thing?