It's possible to achieve this on your first play-through if you import a Shepard from Mass Effect 1, Shepard's starting level in ME 2 is dependent on their final level in ME 1.
Shepard's ME 1 level ----> Shepard's Starting ME 2 Level
No Import/Mass Effect Genesis--------> Level 1
1-49---------> Level 2
50-59------> Level 3
60-------> Level 5
(Note that levels 51-60 in ME 1 are only unlocked after beating that game once)
Each Mission awards a certain amount of EXP depending on the type of mission completed.
Without doing any DLC(Including ones that come standard on the PS3 version like Kasumi and Shadow Broker) You can just barely reach Level 30 during the suicide mission if you import a Level 60 ME 1 Shepard.
If for whatever reason you don't reach 30 after doing all Story,Recruitment,Loyalty,N7,and Local quests, Starting a New Game+ will retain Shepard's current level into a new game where more EXP can be earned.
If you somehow have earned the "Long Service Medal" from Either Completing an imported ME 1 or ME Genesis save or ME 2 twice, All characters from this point onward will get a bonus 25% to all Experience gained, with this bonus reaching 30 without any DLC is very doable without having to use New Game+