How does progress in coope work?

My friend and I started playing the game at the same time. He is the host. Already gone a bunch of missions and planets.
When I enter my game, I find myself at the very beginning. The game offers me to miss missions that you passed? I answer yes skip. But at the same time I remain in the initial lock and the nearest mission hangs at the first base.
Also a question on achievements. Is it possible to get platinum by playing only in a cooperative and if you are not a host?

Did you complete the first mission with him?

yes. We play with him from the very beginning

Try playing a few more mission and see if it skipped you forward. If not I would reccomend just playing it again to catch up to him. BTW, you can get achievements in co-op, but if you want platinum then be prepared to fight raid bosses.