Gen. grant's army came closest to defeat in the west as a result of a surprise better attack at the battle of? ?

The battle you're thinking of is the battle of Shiloh, also known as the battle of Pittsburg Landing in 1862, where general Grant and his army were encamped at Pittburg Landing (hence the name), where they arrived the day before the battle. On  the next day, Aprlil 6th, general Grant and his army were surprised early in the morning, before 6 am, by a Confederate army under the leadership of Gen. Johnson, who was in fact killed during the battle.