The Shooting Range was a subsection of the USM Valor's Armory where off-duty Marines could practice their accuracy and shooting skills on holographic human-sized targets.

Dead Space (2008)

In the original game, after clearing out the Divider (along with its limb-spawns) and several Exploders infesting the room, Isaac can activate the panel on the Shooting Range to begin a shooting program consisting of shooting red targets to earn points and avoiding shooting at blue targets. There are 9 target holders a short distance in front of the standing area and five levels of increasing difficulty to beat to earn all of the prizes, which appear on a small platform in front of the menu screen of the Shooting Range.

By completing the fifth level in this minigame, you unlock the achievement "Crackshot". The prizes are as follows: 

Level 1: Random ammo (Plasma Energy seemed to be the most common)
Level 2: Random ammo 
Level 3: Medium Medical Pack
Level 4: Ruby Semiconductor
Level 5: Power Node

Strategy

• When you play this minigame, you are granted unlimited ammunition (Only for the target range). Fire away!
• Levels are beaten by shooting all of the red targets that appear along with not shooting any blue targets, earning a flawless score in the process.
• As levels increase, you must shoot more red targets that spend less time exposed.
• Use a weapon with instantaneous projectile speed, such as the Plasma Cutter or the Pulse Rifle.
• You get/lose the same amount of points for hitting a target, regardless of where exactly you hit them.
• Standing further back helps as it reduces the time required to sweep the gun from the leftmost target to the rightmost. Standing too far back will immediately exit the mini-game, which in itself can be useful if you miss an early target in the level and want to restart it right away.
• Standing to the side helps as it prioritizes 2/3 of the field. While this does cause the other 1/3 to be harder to hit, this still tips the odds in your favor
• After you've beaten level 5 and acquire the Power Node, don't continue to play any further as you will not get anymore prizes for completing levels 1-5 again.
• Don't worry about dismemberment, one hit fully dismembers a target.
• It is useful to not aim when looking for a target. Since you can just immediately snap to the target by moving the camera to it, then aiming, which is faster than the aiming camera.

Dead Space (2023)

In Dead Space (2023), Isaac is unable to complete the minigame. During round 1, several Twitchers, Lurkers, and Exploders burst through the room. After defeating the onslaught, a voice announces the game is broken and requires maintenance. Isaac can still open many lockers to find bountiful ammo, a Power Node, and a Ruby Semiconductor.

Trivia

• The Shooting Gallery is one of two minigames in Dead Space, the other being Zero-G Basketball.
• In the original game, while the Shooting Range is active, you will have infinite ammo for all weapons. The effect, however, is canceled when the game ends.

Sources