The bottom of that bird's beak is longer than the top part of his beak.
この場合、次のような言い方ができますよ。
ーThe bottom of that bird's beak is longer than the top part of his beak.
「その鳥の下のくちばしは、上のくちばしより長い」
the bottom/top of that bird's beak で「その鳥の下/上のくちばし」と言えます。
ご参考まで!