The following route description has been provided by Shaun Cooney who completed this route with Jon Bradshaw, July of 2016. All photos provided by Shaun Cooney.
From your parking spot along CO Rte 2B @ 11,650' meander your way north into the basin SW of Dyer Peak's summit, commonly referred to as Dyer Amphitheater. Follow a faint trail up the basin until it gives way to rockier terrain above 12,000'. Continue on a general trajectory up the basin aiming for a point of your choosing somewhere between the saddle with West Dyer and the first major rocky obstacle on Dyer's west ridge. The view of Dyer's west ridge from your vantage point in this basin may appear intimidating and/or undesirable at times, but for peakbaggers comfortable with a little bit of scrambling and minor to moderate exposure, the route up the ridge is far more pleasant than it looks from here!
Once on the west ridge's crest, begin your climb. The ridge is interspersed with several rocky ribs which bisect the ridge crest to form several small 'teeth'. These ribs are generally best traversed on the south (climber's left) side of the ridge. The northern side would offer a much more airy challenge! You'll encounter 4-5 major ribs along your route, with each rib offering multiple lines and generally pleasant scrambling ranging from class 2+ to a few short sections that may require a 4th class move or two. The rock is generally solid & secure, but do be wary of the occasional loose handhold. We were generally able to stay either directly on, or near the ridge crest the majority of the way. From the last rib, it's a short stroll SE to the summit on typical Mosquito range talus.
From the summit, the most expedient way down to your vehicle will be to follow the grassy SE slopes back to CO Rte 2B, then hike a short distance back along the road. To take this route, follow the SW ridge off of Dyer Peak for just over 1/4 mile to about 13,500'. Take a moment to observe the terrain. Your goal will be to follow the broad, SE ridge that shows on topo maps. In reality, this ridge is so broad that it can be hard to distinguish, depending on your vantage point. Use your best judgement, and steer yourself down toward the road coming up Iowa Amphitheater below you. Avoid any temptation to veer too far south, as this leads into rocky terrain which contain several small cliff bands. You will be best served by aiming more east than south along your descent and trying to stay near the aforementioned ridge line. The terrain should be mostly tundra as you descend lower, with some interspersed rocky sections. Once you've reached the road, follow it back approximately 1.25 miles to your vehicle.
Links to other information, routes & trip reports for this peak that may be helpful.