It has very little to do with leg strength. If you want to improve your anaerobic work capacity you need to do intervals that target these type of efforts. Do 10 repeats up that hill with 3-4 min of rest between intervals. You may need to adjust your effort so you can get through the 10 intervals.

Just remember that anyone doing an all-out 30-60 second effort feels gassed at the end. The goal is to be able to get up the hill only using 80% of your capacity while everyone else is at 100%. This can be improved by building your threshold power as well as your anaerobic work capacity.

You also need to train yourself to push through the pain and keep the power on once you crest the hill. It will be uncomfortable but you should be able to at least ride at your threshold power after a hard effort up the hill.