Phantasy Star Online 2 New Genesis

Hitting the new level cap means going from the previous one (70) to 75. Assuming you are starting from 70, it's really very easy to accomplish this in a short time. Just hit the current highest rank combat sector (as of writing; Resol Forest) and PSE Burst farm for a bit, or run Stia Trooper with Common Yellow Triggers for a greatly accelerated rush through. Using free boosters you can trade for at the Item Trader makes it even faster.

The issue currently is that the achievement did not unlock automatically for me. I had to visit the Class Counter in the nearest main city location and change classes away from my maxed 75 one and back to it for the achievement to pop. Do this and it should work for you, it is unclear if this is a bug that will be fixed soon.

If you are leveling a much lower level character, I suggest going through the main story tasks normally. They give more EXP per mission now and you can get a chunk of the way through the grind just by doing that.