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Have a friend that's level 28-30 run through it with you on hard. Until you can't do it anymore and then play some crucible. I leveled my second character like that, took around 6-8 hours.
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Clear the story! That should dump you at around level 15 or 16. Then if I were you I'd do some strikes/crucible to finish of the remaining levels you have.
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Do all the missions and pve bounties.