。
She tried to swim across the Thames.
Literal
She [topic-は] Thames-river [traversal-を] swim [then-て] [tried to-cross-渡ろうとした].
泳いで渡る is a manner-and-action chain: te-form 泳いで ('swimming') sets up the means by which 渡る ('cross') happens — 'cross by way of swimming.' The を on テームズ川 is the traversal を, marking the path being moved through (the same use as 公園を歩く 'walk through the park'). テームズ川 is an interesting cross-cultural name: テームズ is the katakana rendering of 'Thames,' and 川 is appended as the type-classifier, the same way アマゾン川 ('Amazon River') or ナイル川 ('Nile River') stack the loanword name with the Japanese kanji for 'river.'