The official walkthrough of this featured HITMAN 2 contract! I say official because I'm the "Franz" guy who created it (it's my nickname on Hitmanforum, where these contracts can be submitted), but there are plenty of other approaches available.
This one shows how to do it without explosions, pistol distractions, sight lures or RNG-dependent mechanics. Foolproof, as some would call it.
Definitely try this out, as well as the other featured contracts.