This achievement is obtained by reaching Level 80.
Leveling up is achieved by completing Wordament puzzles. Wordament puzzles can be completed in Adventure Maps, Daily Challenges and/or Quick Play. The fastest method I found is to just play Wordament Quick Play on Easy setting. The Wordament puzzle words at this setting are merely 3-4 characters long. It took me 6-7 days playing about 4 hours per day to reach Level 100.
Levels/Titles starting at Level 20, as of Version 3.0.51501.0:
Level 20: Skilled
Level 35: Seasoned
Level 50: Pro
Level 65: Advanced Pro
Level 80: Expert
Level 100: Advanced Expert
Level 115: Master
Level 130: Grandmaster
Level 150: Legend
Note/Bug 1: As of Version 3.0.51501.0, the Expert Title is awarded in-game, but the achievement does not pop until successful completion of a subsequent puzzle.
Note/Bug 2: Version 3.0.51501.0, pushed out on Friday May 19, 2017, fixes Title/Level mismatch bugs. If you started working towards this achievement prior to this patch, you will not earn this achievement until you reach Level 100, Advanced Expert.
Note/Bug3: As of Version 3.0.60103.0, pushed out on Saturday, June 3, 2017, it appears that the game is maxed out at Level 150. I.e., you can keep playing, but no additional progress is accumulated and there are no additional awards.