In order to level up your heroes in MAA, as you probably know already, you need not just experience for your team, but also Shield Points to actually purchase the level up. However, it is the experience that matters a lot here, and you should focus on getting it as fast as possible.
You get experience for your team of heroes in Marvel Avengers Alliance by completing missions. There should be a trick to have in mind when playing in order to maximize the XP revenue: remote missions should be chosen wisely: shorter missions when you are online, playing and the longest possible missions (for maximum XP gains) when you’re not playing.
You will also need a lot of energy in the game, so adding more neighbors in MAA to get the energy benefits would be indicated to help you level up faster and constantly in Playdom’s title.
You will also need, as I said, Shield Points in order to complete the level up process and in order to get these, having as many neighbors as possible is also indicated. A good trick here would be to always have Shield Points stacked so as soon as one or more of your super heroes reaches the XP cap to level up, you can start the process right away.
And don’t forget: if you level up faster in the game, your team will only get better!