"Eliminating" is not the right word, since at this point Dugin's ideas will live on in one form or another regardless of his individual fate.
Discrediting Dugin's ideas is what needs to happen, and that would begin with Russia's humiliation in Ukraine.
Can it happen? Who knows?
Here is a list of Dugin's books: 
- Konspirologija (1993)
- Foundations of Geopolitics: The Geopolitical Future of Russia (1997)
- Eurasian Mission: An Introduction to Neo-Eurasianism (2005)
- The Fourth Political Theory (2009)
- Last War of the World-Island: The Geopolitics of Contemporary Russia (2010)
- Putin vs Putin: Vladimir Putin Viewed from the Right (2012)
- The Theory of a Multipolar World (2012)
- Martin Heidegger: The Philosophy of Another Beginning (2013)
- Political Platonism: The Philosophy of Politics (2019)
- The Great Awakening vs the Great Reset (2021)
Among the consistent themes is a geopolitical dualism pitting "Atlanticism" of western style democracies against "Eurasianism", a geopolitical block lead by Russia and opposed to "Atlantic" democracies, especially the US.
Yes, Dugin can seem somewhat sympathetic while criticizing modern "liberalism", which we call "progressivism" or "woke" -- since US conservatives consider traditional/"classical" liberalism (freedoms, free markets, limited government) as the foundations of conservatism and also as impossible to find in modern "progressive" or "woke" ideologies.
Nevertheless, Dugin's critiques of modern progressives in no way make him "the enemy of my enemy is my friend", far from it.
Regardless of how accurately Dugin criticizes progressives, he comes at it from a very different place than traditional US conservatism or even, arguably, from today's populism.
Plus, while Dugin is fearless in condemning western "oppression", he has nothing but kind words for Russia's traditional highly authoritarian aggressiveness such as we see in Vladimir Putin and his invasion of Ukraine.
Final point: Dugin's most recent book, "The Great Awakening vs the Great Reset" (2021) pits two fantasies against each other -- the "Great Reset" from Davos in 2020 and an imaginary "Great Awakening" which, if it happened, would be the fifth.
In reality, the Davos 2020 "Great Reset" is nothing more than slick advertising repackaging a grab-bag of old ideas, none of them particularly threatening, or even measurable.
And the "Great Awakening" that Dugin fantasizes has nothing to do with the previous four, while everything to do with Dugin's support for highly authoritarian and aggressive neo-tsarist "Russkiy Mir" politics.
"Putin's brain", Alexander Dugin: