PIR sensor based LED light controller

You need to be certain on your voltage and current specifications.
You say 150 ma peak load.

If properly configured The LT1302-5 will easily meet your stated need. If it is failing to do so there is either something wrong with your circuit or your load is far greater than you state. The Digikey parametric selector suggests that there are 150 mA and 600 mA Iout versions but this does not appear to be suppoted by the datasheet.

The LT13o2-5 will provide up to 600 mA at 5V out. The graph below (from page 1 of the LT1302 data sheet shows that peak efficiency with vIN = 2v is achieved at Iload ~= 200 mA - above your stated requirement. and they show results up to Iout = 600 mA.

The battery current will be ~+ Iout x Vout/Vin x 1/Z
where Z = converter efficiency (0 <= Z <= 1).
For say 80% efficiency, 2V in and 5V out and 150 mA load, I battery
~= 150 mA x 5V/2V x 1/0.8 =~ 500 mA.
That is well within the capabilities of Alkaline AA cells or of rechargeable NimH cells.
Battery life at 150 mA ~= Battery_Capacity / Battery_Current x K
where K is a derating factor 0 ...1 which drops as load increases and as the battery is used (due to rising internal resistance).

4 x AA cells will provide 5V for only a small part of an Alkaline battery's life and not at all with NimH.
5V/4 = 1.25V
You need at least 1..25V/cell to regulate it down to 5V. Alkaline and Nimh can be considered to be 'dead' at 1V.
So 5 cells and an LDO (low dropout regulator) would be a minimum.
Valkaline_new ~= 1.65V, so initially 5 cells would give you 1.65 x 5 = 8V +.

A boost regulator is not useful here. The problem is that your module, based on the BISS0001 PIR IC, the output pin is VCC (3.3v) 10mA max. Connecting a boost regulator to this output would be really limited.

All you need is a single transistor.

^{simulate this circuit – Schematic created using CircuitLab}

Problem is that you need a transistor that works on the current provided from the output pin. Normally you see a 1k or 2.2k resistor on the board from Pin 2 of the BISS00001 to the output pin, which means only 2ma or 1.2ma at the output pin.

So you need either 1) a Transistor with a HIGH HFE or 2) a Darlington Pair (Two transistors in a pair).

^{simulate this circuit}

These numbers are all based on the transistor you choose. A 2n3904 is only 100mA to 200mA max, with a hfe of 30 (So it multiples the base current, 1mA by 30, and that's the maximum current you get at the collector, 30mA).

You need to know how much current your led box needs, and what voltage it can use. I also assumed that your two batteries are in series.

See this page http://www.electrobob.com/fun-with-leds/ for a project that does both LDR and PIR for leds (but not the same way as what I think you want).

Adding the LDR as a night time detector is simple, and also requires a transistor.

^{simulate this circuit}

Q1 and Q3 can be any weak small signal transistor (2n3904 100mA), Q2 should be a better one depending on your led box current needs (2n2222 1Amp). Adjust R2 for sensitivity.