Playing though the whole campaign on normal with whichever chassis should get you to at least 28/29. Then you can replay the last level 'End User' on easy for 40k xp which should take you to 30 quickly.
Also, you don't have to start from the beginning with a new chassis so to level the others, just grind it out on the last level as above. My lvl 1 Vanguard got to lvl 14 in just 2 runs.