Maybe some player skill, but above all, a good leveled Reflexes (Handgun) skill.
Handguns Skill
Level 5 - Reduces the Spread of your Pistols and Revolvers by 25% (25%).
Level 16 - Reduces the Spread of your Pistols and Revolvers by 25% (50%).
Level 17 - Reduces the Spread of your Pistols and Revolvers by 10% (60%).
Spread - How far will bullets scattered away from where you were aiming.
And also, for the 1-2 seconds lost, if it's like Stadium Love (not sure), don't try to draw your weapon yourself. Just let the game do it for you. But I say that, not by experience, I'm too bad for aiming, I never "win" it and probably I'll never "win" it
Edit : even more if you aim with the HUD sight only, without Spread reduction, bullets goes wherever they want