'The Dagger of Kamui' is a kind of samurai/ninja story set against the upheaval of the collapse of the Tokugawa shogunate in 1868 and Japan's restoration under the Meiji Emperor.
Literal
'Kamui no Ken' [topic-は], 1868-year [genitive-の] Tokugawa shogun era [genitive-の] collapse [and-と], Meiji Emperor under [at-での] Japan [genitive-の] restoration [called-という] transformation-period [object-を] stage-set-on did, one-kind [genitive-の] samurai/ninja story is.
A long descriptive sentence with several layers of modification. The ~という変革期 ('the transformation period called/consisting of...') bundles two coordinated elements (徳川将軍時代の崩壊 and 明治天皇下での日本の復興) into a single noun phrase, then という re-labels them collectively as a 'transformation period.' That entire phrase is then the object of 舞台にした ('made the stage [of the story]'), which itself is a relative clause modifying 物語. So you read it inside-out: a 'samurai/ninja story' → 'set in a transformation period' → 'consisting of [collapse of shogunate] and [restoration under Meiji].' での is the locative で plus genitive の, marking 明治天皇下 ('under the Meiji Emperor') as a contextual location for 復興.