This is one of the easier achievements in the game. Simply select "Draft Champions" from the main menu. If this is your first time, a few tutorial screens will pop up, after navigating through these, you'll be asked to select the theme of your draft team from 4 different options (this determines the players available in the draft to you). At this point you'll begin drafting a team of players (cards) that will make up your Draft Champions team. Simply complete all 12 rounds of the draft and your achievement will pop.
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Note: this is the beginning of draft champions and this teams is what you will need to use to complete the "All the Way!" achievement. Each draft champions draft has 4 games you can play with the team you draft. You'll need to win all 4 with a decent team. If you lose any game along the way, you'll need to re-draft a new team, so pay attention to the team you draft and aim to win!