Levels are gained through experience received from kill enemies, picking up green experience drops, and the XP Boost perk. Through normal play, you should reach level 30 at around 30-40 minutes. As you progress, zombies earn you the same amount of experience that they did at the beginning, but the green XP drops actually scale based on the length of time you've played in the current session. At around the 25 minutes mark, XP drops will start to give you whole levels, making them your primary form of experience gain. After the second boss is defeated at around 25 minutes, there will be a large number of XP drops all over the arena, each awarding a whole level. Keep an eye out for these as you play and this trophy should come naturally.