If I play Krenko, Mob Boss and retain priority and cast Swiftfoot Boots on Krenko Mob Boss and at the same time my opponent casts Unsummon on Krenko Mob Boss, will my creature be safe or will he be removed from the battlefield?
If I play Krenko Mob Boss and retain priority [...]
First, let's clear up this confusion. If you cast Krenko and retain priority, then Krenko has not resolved. You need to wait until after Krenko resolves, at which point you will have priority because you are the active player.
Now, after Krenko resolves, you decide to equip Swiftfoot Boots to Krenko. Equip is an activated ability. That means it will not resolve until all players pass in succession.
702.6a Equip is an activated ability of Equipment cards. “Equip [cost]” means “[Cost]: Attach this permanent to target creature you control. Activate this ability only any time you could cast a sorcery.”
608.1. Each time all players pass in succession, the spell or ability on top of the stack resolves. [...]
Your opponent may choose not to pass, and cast Unsummon instead. If they do that, then Krenko will be returned to your hand. Then, the equip ability will attempt to resolve, but will fail because Krenko is gone. Here's a little diagram to illustrate the process:
activate ability -> stuff happens -> ability resolves if target is still legal
Casting a spell uses the stack just like activating an ability does. Your opponent will get an opportunity to respond with Unsummon. Because Unsummon is instant speed, it can be cast when there are other items on the stack. However, casting an artifact spell or equipping a creature with equipment is a sorcery speed action and therefore can only be cast on your turn when the stack is empty.
Let's say you attempt to equip Swiftfoot Boots to a creature. The equip action actually goes on the stack. Then your opponent can respond with Unsummon. The stack will then look like this:
Unsummon will then resolve first because it's on top of the stack. This is before your creature gains hexproof. Your creature will return to your hand. The equip action will fizzle because the creature it was targeting no longer is a legal target.
Krenko will be returned to your hand. However it should be noted that you cannot cast a Swiftfooot Boots on any creature, you need to have already cast the boots then pay the equip cost to attach them.
Priority doesn't seem to work the way that you think it does, the Unsummon does not happen at the same time as the Equip, it happens in response to it. If you cast Krenko and retain priority you need to then cast an instant (or activate an ability), Krenko will not resolve until all players have passed priority with Krenko being the top thing on the stack. Once Krenko resolves you automatically regain priority (assuming you are the active player), at this point you can activate the Equip ability of the Swiftfoot Boots targeting Krenko.
At this point you need to pass priority to your opponent, rather than passing priority back and letting the Equip ability resolve they instead choose to respond with Unsummon also targeting Krenko and pass priority back to you.
You now have the opportunity to respond with your own spell (or activated ability), and if you choose not to the first item on the stack will resolve, in this case the Unsummon returning Krenko to your hand. Assuming you and your opponent both pass priority again the next thing on the stack will resolve, this time it is the Equip ability. Since the Equip ability no longer has a legal target the ability fizzles and does nothing (if it was attached to a creature prior to activating the ability it will still be attached when the ability is countered).