We have sequenced Mt. Champion with UN13,736 and Deer Mountain on a long ridge connect. Combining these three summits makes for a longer and more difficult day, hence the "Long Day/Back for Dinner" rating. The only real problem with climbing Champion is the initial start and heading up Lackawanna Gulch. This initial start is the same as we have for K49 (UN13,535). Our route described here is best suited for West Slope hikers, but the trailhead access for Front Range hikers, involves probably a little more driving time than taking the long dirt road up Halfmoon Creek out of Leadville.
From the trailhead, walk north on the old roadbed a few hundred yards and find a place to ford the creek. Once across, follow an old jeep track north into a clearing with some old mine tailings. Locate a trail that continues north, then turns east climbing into the trees. This trail continues well-defined (as of 1989) up into Lackawanna Gulch. Eventually, it fades in the higher meadows as you approach timberline. Bill Middlebrook on 14ers.com refers to a more ill-defined trail here. This may be the same as we have described, but what we found was never sketchy at the time. The main point is to work your way east, up through forest and staying on the north side of the main creek in Lackawanna Gulch. It's probably best to avoid the temptation to head directly up the SW ridge of Champion. Continue along and above the creek to about 11,300 feet in elevation where trees begin to thin. Turn more to a NE heading and begin hiking much more steeply up the south slopes of Champion. It is not necessary to continue east up Lackawanna Gulch until the stream forks, but you can if you find using the trail easier.
Once you depart the trees, heading north up the steepening south slope, the remainder of the hike is uneventful. The ground coverage is mostly tundra/grass for quite a ways before getting into more scree/rock, etc. Pass the old Champion Mine at about 12,900 feet. At about 13,500 feet, you'll intercept the SE ridge coming in from the right. Continue north along the main ridge to the summit and an impressive view gazing down into the North Fork of Lake Creek, now 2,000 feet below.
For the descent, return as you came. For the more determined peakbaggers, continue north from Champion and begin the trek to UN13,736 and Deer Mtn. The next couple hours of hiking will be a ridge type "skywalk" with impressive views on either side.
Links to other information, routes & trip reports for this peak that may be helpful.