。
She's taking on one debate after another.
Literal
She [topic-は] one-after-another debates [to-に] is-challenging.
論戦 ('debate, battle of words') is a vivid Sino-Japanese compound — 論 ('argument, discourse') + 戦 ('battle') — that frames intellectual debate as combat. 挑む ('to challenge, to take on') takes に for its target — challenging at, going up against. The progressive ~ている paired with 次々と paints an active, ongoing series of confrontations. The と variant of 次々 has the same meaning as 次々に but with a slightly more vivid, narrative feel.