The advance in the heavyly damaged(大破) state may let KanMusu sink. They don't sink if it's minor damage(小破) or moderate damage(中破).
1-4 is the first barrier in KanColle. You must challenge it by the strongest fleet which oneself has.
Do you have CV(Aircraft Carrier) or CVL(Light Aircraft Carrier)?
Class classification
http://kancolle.wikia.com/wiki/Glossary#Class_classification
Do you make various airplanes with development?
(Fighter, Dive Bomber, Torpedo Bomber)
Equipment List
http://kancolle.wikia.com/wiki/Equipment
Do you perform various quests?
Quests List
http://kancolle.wikia.com/wiki/Quests
You get carrier Akagi if you achieve Quest A-11 and B-10. At first let's prepare Akagi and airplanes. It's a course to 1-4 clear.
- A11: 第2艦隊で空母機動部隊を編成せよ! Have an aircraft carrier/light aircraft carrier and 3 destroyers in your SECOND fleet.
- B10: 敵空母を撃沈せよ! Sink an enemy aircraft carrier.
Well, What character is your avatar? She is very cute :P