In the beginning of the Sword Art Online anime, episode 2 "Beater", Kirito acquires the Coat of Midnight when getting the last attack bonus on the boss.
Up until episode 7, "Warmth of the Heart", it appears he is using mostly the same gear. In the beginning of this episode when we first see him, he is daunting a new coat and his Elucidator sword. Lizbeth does say, "this is the gnarliest sword you can get from a monster drop" or something to that effect.
Is there ever any mention of where/how he acquired his new gear? I haven't read the manga series, is there any mention in it?