so sudden or so suddenly?

Both are correct!

sudden 是 adjective，用來形容名詞(noun)；
suddenly 是 adverb，用來形容動詞(verb)、adjective等等。

（其實分別跟 happy 和 happily一樣。）

例子一：
His jump is so sudden that I cannot react promptly.
（他的跳躍太突然，我來不及反應。）
〔這個jump是名詞。〕

He jumps so suddenly that I cannot react promptly.
（他跳得太突然，我來不及反應。）
〔這個jump是動詞。〕

例子二：
We were all shocked because his death was so sudden.
We were all shocked because he died so suddenly.

So Sudden

兩個都可以是正確

原則是文法上仍是依據
形容詞sudden要形容名詞
副詞suddenly要形容動詞

His move was so sudden.
sudden形容的是他的move(名詞)

He moves so suddenly.
suddenly形容的是他move(動詞)

[一般你見move字用法是動詞，特別選用這字作兩句來讓你看這分別用用法的精義]