It took me 96 matches to unlock the helmet, steps 3 and 5 took the longest for me. The helmet is ridiculous, its bad enough losing only earns you 2 percent completion but winning also earns you 2 percent completion. The only way for me progression is winning streaks, which are hard to get when bungie makes sure you are playing against people at your skill level or higher. In the end it took me 40+ matches to unlock the helmet.
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I heard that last step could be done via public events too. I highly doubt it though