There are many special achievements in "Silent Hill 2: Remastered (SILENT HILL 2)", and Stealth Approach is one of them. The requirement to achieve this achievement is to complete it without using long-range weapons to kill the enemy. In the game, this is still very difficult. You can still use a chain saw in the second game.
How to get the Stealth Approach achievement in Silent Hill 2
Lurkingly approaching
Complete the game without killing an enemy with a ranged weapon.
Use the Chainsaw (NG+ weapon) to easily complete the game in NG+ defeating enemies using only melee weapons. Note that common melee weapons like wooden planks and steel pipes are already powerful on light combat difficulty, and defeating enemies (including bosses) with these weapons won't take much time.
Shooting a gun will not invalidate the achievement as long as you don't kill any enemies. Photographing windows or balloons is allowed (see the achievement "We Don't Want a Party!").
This achievement can be obtained in NG+.