Should I use an LP2953 to power an ATTiny85 with a 12v battery?
Unfortunately a linear regulator is a linear regulator - it drops the excess voltage and dissipates power as heat ... so just like the 7805 you had, the LP2953 is still a linear regulator.
12V in to 5V out makes it never much more than about 40% efficient, so however much power your ATTiny is using - 1.5x that is being wasted as heat in the regulator.
You could improve the regulator efficiency and reduce wastage significantly by using a DC-DC switch-mode regulator instead. They're more complicated to build from scratch, but ready-made modules are available - some are even drop-in replacements for the 3-pin 78xx linear regulators.
Chose the right one and you should easily get 80% or better efficiency from it.