Pestering with a mite.

[Desolatus]

Can I tap to attack say, oh, a Prime Time, then flash in {Pestermite}, untap the Titan, then attack again to another player? It's a long shot, but I have hope.

[BlackJester]

Can I tap to attack say, oh, a Prime Time, then flash in {Pestermite}, untap the Titan, then attack again to another player? It's a long shot, but I have hope.

Hope is lost.  No.

you have to declare all attackers at once before you can cast instants and use abilities.  Once you've declared, you can't declare more.

[Willthomjr]

Can I tap to attack say, oh, a Prime Time, then flash in {Pestermite}, untap the Titan, then attack again to another player? It's a long shot, but I have hope.

You must declare all of your attackers at the same time. So no it will not work.

[Desolatus]

It was worth a shot.

[Gorzo]

You can however attack a second time with special spells and abilities that allow you to do so, such at {World at War}, {Hellkite Charger}, or {Finest Hour}.