There were a number of military challenges that faced President Lincoln over the course of the Civil War. Among these challenges were:
The simple fact that the North had to invade the South to win. The North could not simply fight a defensive war like the South could have done. Instead, it needed to invade and subdue the South. Mounting a successful invasion and conquest is always much more difficult than defending against one.
Lack of a solid officer corps. The South had been a much more martial society before the war. This meant that many of the best officers in the antebellum US Army were Southerners and went with the Confederacy when the South seceded. The greatest example of this is Robert E. Lee.
Difficulty in finding generals who would carry out his strategy. One of the best-known problems that Lincoln had in the war was finding competent generals at the highest level. The most famous example of a general who failed Lincoln was General George McClellan. His unwillingness and inability to pursue the strategy that Lincoln wanted was a major difficulty for Lincoln in the war. Lincoln would not solve this problem until he found General Ulysses S. Grant and installed him as the main commander for the rest of the war.