There are 6 sections to the tutorial for Might and Magic: Duel of Champions. In each one they will introduce a new aspect of the game and then set you free to defeat your enemy with what you have just learned. The first 5 sections deal with attacking and defending with creatures, casting spells, and increasing your resources. The 6th Battle is just a single player duel against the AI without any help or tips. You will be allowed to choose 1 of 6 starter decks each with its own strengths and weaknesses. Just defeat your opponent and the achievement is yours.
After each of the 6 sections you will be receiving xp and gold. You should also unlock the "The Stable Hand" achievement for reaching level 2 at the end of the tutorial.