Depending on your tolerance for this sort of nonsense, grinding level 6 2x xp missions may be the way to go for the level 25 trophy. I've been running them offline and it takes on average 6 minutes to finish one for 4400 xp. The level 12 missions are triple that at around 13k, but that assumes no deaths, all objectives complete and all extracted.
So, if a team of 4 can successfully finish a level 6 in that same 6 minutes, to make it equal they'd have to finish level 12 helldives perfectly in 18 minutes. That has not been my experience what with the chaos and all. Level 9 might be a good middle ground (maybe 8k xp?) but I can't do that solo to find out. The higher difficulty of war #2 isn't helping, so maybe the war reset will make it easier.
It's still a long ass grind to 770k xp - from where I'm at (mid level 22) I'd need around 90 of the level 6 missions or around 10 hours to finish. I don't know where the timer is on the war reset, but if it's already lost tonight might not be a good night to get a tank since whatever faction you can get a tank from might not be available yet.