Learn Icelandic: Hún hefur bætt metið hans. - She has improved his record.

Bæta (to improve) is a Group 2 weak verb. To make the supine (sagnbót) for this group, you normally take the stem and add -t. The stem of bæta is bæt-. When you add -t to a stem that already ends in a -t, you get a double -tt, resulting in bætt.

Why is the translation "his record" written as metið hans instead of hans met?

In Icelandic, it is standard to put the possessive pronoun (like hans) after the noun. When you do this, the noun must take the definite article. So you literally say "record-the his", which gives us metið hans.

Why doesn't the word metið change its ending here since it is the object of the sentence?

It actually is in the accusative case because it is the direct object of bæta. However, met is a neuter noun, and neuter nouns always have the exact same form in the accusative case as they do in the nominative case. The -ið is just the neuter definite article.

Would bætt change its ending if the subject were plural, such as "Við höfum..." (We have...)?

No, it stays exactly the same. When you use the helping verb hafa (to have) to talk about something that "has" happened, the main verb is always in the supine form. The supine never changes to match the subject's gender or number.