。
She holds very radical views on that issue.
Literal
She [topic-は] that issue [about-について] very radical opinion [object-を] is-holding.
過激 ('radical, extreme, militant') is a na-adjective with a notable political tilt, often appearing in 過激派 ('extremist faction') or 過激な発言 ('extreme remarks'). Stronger than 強い意見 ('strong opinion'); it implies departure from mainstream views, sometimes with a faintly ominous tone. 意見を持つ ('to hold an opinion') in the ~ている form expresses 'has the opinion (held over time)' — the closest Japanese equivalent of English's 'has an opinion.'