fist of all:
for the spartan officer achievement, u need 50 exp in one playlist. I did it on ranked team slayer but i suggest lone wolves if u alwaysd get a team who sucks.
and last:
for the katana, all u need is to get at least 40 achievements (that includes the updated ones) and 1000 gamerscore. I think it may have changed that all u need now is 1200 gamerscore ONLY but someone please check this as im not sure if im right. as long if u have at least 40 achievements and 1200 gamerscore, u should be alright.