Dragon Age: Origins

There are two ways to get this. One - play the game like you should, fight as many enemies as possible and do as many sidequests as possible. I got my level 20 towards the end of the game.

The other way to do it is to get to Ostagard and start the quest where you get three vials of darkspawn blood. Get those three vials but don't get the treaties. Return to Duncan and tell him you have the vials but not the treaties. You will receive experience. Now keep talking to him stating the same thing, you will continue receiving experience. Grind up to level 20 and enjoy achievement goodness.

If you own the the Golems of Amgarrak or Witch Hunt DLC, there is a very simple way to get this achievement. Simply start a new mage in Origins and save the game. Then, start a Golems of Amgarrak/Witch Hunt save file and import this character. Skip through the cutscenes and dialogue. Since all characters in Golems of Amgarrak/Witch Hunt start at level 20, all you need to do is "level up" and the achievement is yours.

[[Thanks to Mike Marcelais]]

One additional note to Minioger's solution: the achievement only unlocks after you "level up" with the A button from the stats screen. There is a glitch though -- if you don't level up when you're exactly on level 20, the achievement will never pop. I overshot and didn't level up until level 21 and learned this the hard way.

Just a note; this can be obtained in Awakening, on all 3 classes. Just hit 20 in Awakening and level up, few seconds later the cheevo will pop up.

If you have Witch Hunt DLC, this will take you only couple of minutes. Forget what some other people say about starting a character in Origins and then importing it into the DLC.
Simply start new game on Witch Hunt DLC, select option to create new character, make sure to select "Mage" as your character class and then after selecting your faction (Grey Warden should be the only option) hit "Y" to "quick start." The achievement popped for me on the loading screen right after, before the opening cut scene.

While playing through Dragon Age: Origins I stumbled across a small unpatched glitch which can be exploited over and over again effectively granting the player infinite experience points. This specific XP glitch is new to me, I haven’t seen it anywhere else, so here it is. It has some minor spoilers about the storylines that take place in Orzammar because you have to make specific plot choices to access the infinite XP glitch, so if you don’t want to see this information then do not read on.

To gain access to the glitch, you have to acquire the quests to support both Lord Harrowmont AND the quest to support Bhelen. To do this, tell the dwarf in Lord Harrowmount’s estate that you will support Harrowmont, and then tell Bhelen’s representative in the Chamber of the assembly that you will support Bhelen. Do not do any of Bhelen’s requests! These consist of delivering 2 notes.

Go to the Proving and complete Harrowmont’s requests, supporting him entirely. Return to Bhelen’s representative in the chamber of the assembly and speak to him. He will ask why you lied and did not support Bhelen, tell him you did this so Harrowmont will not suspect you as a spy and he will then ask you to share whatever Harrowmont is planning next. Go to Harrowmont’s estate and speak to Harrowmont, he will tell you to kill the rouge Jarvia. Next, return to the chamber of assembly and tell the dwarf Harromont’s plan. He will then ask you to plant papers on Jarvia’s body once she is dead, making Bhelen appear to be the better leader, Agree to do this! Go to Dust Town and kill Jarvia, then plant the papers inside her wooden chest. Go back to the Chamber of the Assembly, and before talking to Bhelen’s representative, save your game just to be safe.

Tell him you planted the papers on Jarvia and He will tell you that it is now time to see Bhelen in person. Choose option #2, which says you need some more time before seeing Bhelen. You can then talk to this dwarf again and again telling him each time that you planted the papers and choosing the option that you are not ready to see Bhelen. You will receive the XP for completing the quest every time; just save often because if you accidentally choose any dialogue option other than the Im not ready yet option you will go to Bhelen and lose this glitch. You get a substantial amount of XP from this, so leveling up can be done rather quickly and it levels up each member of your party as well as your character so its very helpful, I can confirm that this works as and while doing it I went up at least 3 levels every ten minutes or so.