Why don't you get shiv is probably a question you are asking while looking at this build and it has a simple answer. The devourer and berserkers give you the attack speed you need and your q gives you the crit on next attack. The reason for getting hydra is simple. Shaco is a highly burst assassin and not a sustained damage champion so getting lifesteal is almost useless since everyone will be dead before you need to lifesteal. Even if their is a time where you need lifesteal this is easily avoided by dodging and tricking your opponents with your ult and q.

Trinity is amazing on shaco because it gives him everything he needs ( health, crit, damage, a little ap, and movespeed). trinity also has the added bonus of rage which makes you move faster on AA while you have spellblade to go nicely with your passive and next crit on use of q. Frozen mallet is an excellent choice because it gives you a good amount of health with damage and a slow added on. You might be asking why you need that slow if you have your red buff and two-poison shiv (e). yet again the answer is simple your e has a cooldown and cannot be relied on at all times while red also has a time where you will not have it (also it will ,in most cases be a better decision to give to your adc since most of them wont have a reliable slow). Frozen mallet is much more reliable since it works off of your auto attacks which are always up.

Getting devourer has a simple answer. You get it because as shaco you are a very greedy jungler who gets kills from invading and ganking and one who farms a ton until you are fairly unkillable. Once you reach this farily unkillable stage you devotes your time to picking and pushing since you have nice push with ult and boxes.