Approximately how many battles did General Eisenhower loose vs. win in
WW2? And what was the biggest battle he lost?

During WWII Eisenhower's primary role was that of a Theatre Commander
and as such it is difficult to define battles which he "won" or "lost"
as he left detailed tactical decisions to his subordinate generals.
Here is an extract from a piece analysing his military career

"Sicily and Italy offered small opportunity for Eisenhower to display
whatever maturation his more technically military capacities had
undergone through enlarged experience. The geographic arenas were too
narrowly constricted to permit much operational or tactical, let alone
strategic, innovativeness or flair. As with North Africa, the
principal comment to be made about Eisenhower's leadership in its
primarily military aspects must be somewhat negative. He continued to
act on the premise that the supreme commander ought to leave detailed
combat decisions to his subordinates who were closer to the scene of
action. The premise has much to recommend it, but questions arise over
what is a matter of detail. In North Africa, Eisenhower's aloof­ness
allowed faulty troop dispositions to set up a near?' disaster at the
Kasserine Pass and thereby suggested he might be holding himself too
far above the battle. Similarly, in Sicily his aloofness permitted his
senior American subordinate, Lieutenant General George S. Patton, Jr.,
commanding general of the Seventh United States Army, to mount a
series of disproportionately costly amphibious assaults across the
northern coast of the island whose price in casualties seems all the
more disproportionate since the principal end to be served was to win
a race against General Sir Bernard Law Montgomery and the British
Eighth Army into Messi­na."

The full text can be found here

http://www.ksu.edu/history/specialevents/Eisenhowerlecture/eisenhower4.htm