Up to date solution as of June 2020
This achievement's criteria was changed when the game went free-to-play. DrOp ShOtKiNg24's solution is the only other one that's up to date, but doesn't have a lot of details so I'm posting this one.
You can only obtain this achievement on a character created after the release of New Light (when the game went free-to-play), or an imported D1 character that you didn't play on before New Light. This is because the New Light quest isn't available to existing characters. This may be a bug (https://www.bungie.net/en/Explore/Detail/News/48293
) so please comment if you find a way around this for existing characters.
You need to progress the quest Main Quest: New Light
. The first major objective is to reach power level 770. If you're new to Destiny 2, your power level is a function of the level of all your weapons and armor, so equipping a piece of gear that's higher level than what's currently in that slot will increase your power level. You start off at 750, so you should be able to hit 770 after just a few hours of play. Pick up one of the planet introduction quests and work on it. You should get plenty of new gear along the way.
After hitting 770, you'll be asked to speak to Lord Shaxx at the Tower. He'll give you a quest Introduction: Crucible
, which has two steps. First you'll need to complete a Crucible match. Then go back to Shaxx, and you'll get another step to complete a Crucible bounty. Grab all the bounties he has, play a match, and complete at least one of them and turn it in. Then go back to Shaxx to finish the quest and claim a Legendary Engram.
The achievement should pop at this point. If it doesn't, go to settings, change profile, then go back to the character that you were just playing on and it should pop.