Possible Clues:

• The First Lady might have a high old time on holiday up there
• Mountain called Chomolungma in Tibetan
• To get on top of it the girl must take a break
• Would a vest e'er be needed by one up there?
• The lady might have high holiday here
• Mount, climbed 1953
• Challenge for Hillary
• Always set crooked - the very height of it
• One conquered in 1953
• Always it is in Latin and it's tops