Ok, I have noticed that winning or loosing a scenario doesn't seem to make a difference on the number of Insignias you get... it seems to be random 1-3 Insignias for each scenario completed. Emblems seem to drop based on your participation / damage.
Anyway, if you assume an average of 2 Insignias per scenario completed, you will need to do:
160 SCs for your Conquerer weapon
177 more SCs for your Invader Weapon
195 more SCs for your Warlord Weapon
213 more SCs for your Royal Weapon (total of approximately 745 Scenarios)
I have some advice when doing these. AS SOON as you have 320 Conquerer Insignias, go get your weapon. Once you do, you will start gaining Invader Insignias. If you don't, you will continue to get more Conquerers... And... Warning... they only convert DOWN at a rate of 1:1