First set of quests:
You must finish all 4 tutorial missions.
Second set of quests:
1-Complete mission 1(Ruin City) on very easy mode.
2-Complete mission 2(Shuttle Base) on very easy mode.
3-Complete mission 3(Canyon) on very easy mode.
4-Complete mission 4(Test Factory)on very easy mode.
5-Complete mission 5(Lunar Base) on very easy mode.
Third set of quests:
1-Complete mission 1(Ruin City) on easy mode.
2-Complete mission 2(Shuttle Base) on easy mode.
3-Complete mission 3(Canyon) on easy mode.
4-Complete mission 4(Test Factory) on easy mode.
5-Battle in PVP mode 4v4 3 times, doesnt matter if you win or lose just battle 3 times
6----------------------
quest 6 i didnt figure it out yet
@Vivid.Angel: to access pvp you must level up once ^^ just play few missions.