I beat this challenge with a Bant deck, after a hundred tries. The only way to beat the Archenemy, I found, was to Tinker for a Blightsteel Colossus - which I luckily managed to do in my winning run, followed by a Time Walk to make sure the Archenemy couldn't remove it

;Archenemy UGW
;
;User
;User E-Mail
;23/02/2012
;1
;4th Edition
;
.10826 1 Blightsteel Colossus
.10971 1 Batterskull
.166 1 Mox Jet
.165 1 Mox Emerald
.167 1 Mox Pearl
.168 1 Mox Ruby
.169 1 Mox Sapphire
.1207 1 Solemn Simulacrum
.10943 1 Sword of Feast and Famine
.6746 1 Sword of Fire and Ice
.7363 1 Umezawa's Jitte
.10820 1 Wurmcoil Engine
.1351 1 Tinker
.249 1 Time Walk
.1 1 Ancestral Recall
.1528 1 Mystical Tutor
.11183 1 Delver of Secrets
.3716 1 Fog Bank
.11674 1 Phantasmal Image
.11337 1 Snapcaster Mage
.8893 1 Sower of Temptation
.10776 1 Steel Hellkite
.6919 1 Trinket Mage
.9081 1 Vendilion Clique
.17 1 Black Lotus
.230 1 Sol Ring
.985 1 Bribery
.44 1 Control Magic
.10296 1 Jace, the Mind Sculptor
.11327 1 Silent Departure
.11112 1 Vapor Snag
.1341 1 Treachery
.1488 1 Flooded Strand
.438 1 Library of Alexandria
.1487 1 Polluted Delta
.1216 1 Seat of the Synod
.10128 1 Misty Rainforest
.1474 1 Wooded Foothills
.126 3 Island
.377 1 Maze of Ith
.1192 1 Worship
.290 1 Wrath of God
.1560 1 Path to Exile
.240 1 Swords to Plowshares
.10043 1 Day of Judgment
.9584 1 Elspeth, Knight-Errant
.10090 1 Journey to Nowhere
.8859 1 Oblivion Ring
.11002 1 Elesh Norn, Grand Cenobite
.10865 1 Hero of Bladehold
.10887 1 Mirran Crusader
.3966 1 Mother of Runes
.11395 1 Baneslayer Angel
.10357 1 Stoneforge Mystic
.12110 1 Edric, Spymaster of Trest
.9921 1 Jenara, Asura of War
.9791 1 Knight of the Reliquary
.1368 1 Loxodon Hierarch
.9960 1 Qasali Pridemage
.9810 1 Noble Hierarch
.9816 1 Progenitus
.2894 1 Natural Order
.15 1 Birds of Paradise
.8667 1 Tarmogoyf
.1219 1 Ancient Den
.1217 1 Tree of Tales
.10012 1 Arid Mesa
.1716 1 Breeding Pool
.11243 1 Hinterland Harbor
.8574 1 Horizon Canopy
.11288 1 Moorland Haunt
.740 1 Pendelhaven
.212 1 Savannah
.10170 1 Scalding Tarn
.11484 1 Sunpetal Grove
.1499 1 Temple Garden
.1473 1 Windswept Heath
.254 1 Tundra
.252 1 Tropical Island
.10256 1 Celestial Colonnade
.1205 1 Seaside Citadel
.10354 1 Stirring Wildwood
.188 2 Plains
.91 2 Forest
.10763 1 Seachrome Coast
.10973 1 Birthing Pod
.10 1 Balance
.22 1 Blue Elemental Blast
.3021 1 Gemstone Mine
.694 1 Karakas
.11427 1 Glacial Fortress
.1714 1 Hallowed Fountain
.10752 1 Razorverge Thicket
.9363 1 Archon of Justice
.260 1 Unsummon
.4035 1 Academy Rector