This goes by the in-game tracker so be aware that you may have to level up more than 30 champions to level 20 for this to unlock. For whatever reason, 3 of my champions didn't register as over level 10 so I had to level 33 champions up for that achievement to unlock. This seems to be an issue mainly for those that played the game on release. Thankfully I haven't heard of anyone having issues with this achievement unlocking later than expected. Keep an eye on the in-game tracker as that is what will trigger the achievement.
Champions gain levels much faster than previously due to the most recent patch. Additionally, you can spend gold to level up a champion if you have no desire to play them or simply want to speed up the achievement.
It costs 1,000 Gold to buy 20,000XP. Gold is earned through completing daily logins and quests, 1st wins of the day in PVP modes (3 total: Siege, Deathmatch and Ranked), match completions and increasing your player level.
This translates to the following purchases:
level 0-10: 55,000 Gold
Level 10-15: 65,000 Gold
Level 15-20: 90,000 Gold
You can boost the amount of XP & gold you get in a few ways. You get a 10% boost to Gold, Champion XP and Account XP for playing with at least 1 friend in your party. A new booster called a Battle Pass has been added which costs 500 crystals for 1 'Season' or $39.99 for the Season Pass (3 seasons of Battle Pass). Although there are other cosmetic reasons one may want the Season Pass - 1500 crystals is currently going for $24.99 so you can get the same boost for much cheaper if that's the route you want to take. Its a 50% boost to gold & XP.
We noticed during this triple XP event that's currently ongoing (May 12th) there is a daily cap on gold earned. I'm not certain what this is but we believe it to be in the 70,000 range.
Long story short, its still a heck of a grind, but you may find yourself in a better situation due to a stockpile of gold. Having them reduce the amount of XP required per level was a godsend for us and this brings the overall completion well within the realms of possible for those willing to spend a few hundred hours playing.
Of note, this is possible to work on entirely in Training matches. Those are where players are matched up to form one team and bots play the opposing side. If you aren't matched with a full lobby within 15 seconds, it will start with whomever it has found - including just you and a team of bots if that is all it can muster. This can be further altered by changing your region in the 'Play' menu. The Brazil server is dead if you are looking to run solo as most Brazilians are actually on the North American server.