Don't listen to the answers/comments claiming that the issue is with your boost converter, as they're incorrect. Your boost converter is more than adequate, one only has to actually read the specs/datasheet to confirm this.
The boost converter you're using has a 4A switch capable of 4.5A surges, and is very efficient even under heavy load thanks to the synchronous rectification. And at 700kHz, the ripple current will be small and the needed inductance will be tiny, so the inductor is plenty large enough to handle 4A+ without saturating. And beyond that, Adafruit themselves specifically specify that converter as being able to handle 4A of input current in the description.
Now, the recommended peak current capability for a power supply that is going to power an Raspberry Pi 3 B+ is 2.5A. Can your boost converter provide as much as 2.5A at 5V? Let's ask Texas Instruments:
Yes. Yes it can. Granted, it needs a fairly stiff input voltage of ~3.9V, but this is well within it's capability. A 3.7V LiPo battery outputs an average of 3.7V. At full charge, its terminal voltage is 4.2V. Also note, this is continuous output current. The actual current draw of a Raspberry Pi B+ is considerably less, the 2.5A power supply is for a 'desktop' configuration, where the USB ports are providing downstream power to connected devices, etc.
Now, back to your problem, why is it boot looping? Well, the answer is because the power supply is inadequate - but the problem is your battery, not the boost converter.
The 3.2V warning LED already tells you all you need to know - the battery voltage is dropping below 3.2V. This happens due to its internal ESR, which acts like a resistive voltage drop, reducing the terminal voltage. The boost converter is quite potent, and is handily sucking out 4A+ from your battery, doing everything it can to boost the output up to 5V at over 10W, but as we can see from the earlier chart, the maximum output current at lower voltages falls off below what the RPI likely needs as surge current during boot up. This causes the boost converter's output voltage to fall, and the RPI doesn't get the voltage it needs, and starts to glitch. The result: an infinite boot loop.
However, even if you use some sort of monstrous 40A input multiphase boost converter, it won't do you any good, because the boost converter is not the problem.
Your battery needs to be able to tolerate 4A discharge current. You need a high-drain, low ESR type of LiPo battery, or simply a larger (physically and in terms of capacity) battery which can handle higher discharge currents with less terminal voltage drop. Keep in mind that you like won't be able to access all of your battery's capacity without a slightly beefier boost converter, but the one you're using is certainly enough to run off a LiPo cell at least while the voltage stays high enough - probably above 3.6V.
The battery you've selected is rated for a maximum of 0.5C discharge current, which is 2A. You're seeing such a huge voltage drop on your battery because you're trying to discharge it at twice the maximum discharge current. This is a potentially dangerous thing to do to a LiPo cell, and you're running the risk of sending it into thermal runaway and starting a pretty nasty fire. Do not continue attempting to use that LiPo cell in this application, and I would recommend you discontinue use of that specific cell completely - its possible that you've already damaged it internally, and it might fail unexpectedly at some later date. And by fail, I mean spectacularly with fire and lots of it. The electrolyte inside is volatile and flammable, the dangerous energy isn't the electrochemical energy in the cell - it's the energy resulting from burning flammable chemicals that tend to get ignited once they're exposed to the oxygen in the air that are normally sealed inside the cell. Just be careful.
So, in short,
You must get a beefier battery, one that can handle in excess of 4A. Don't get one rated for 4A, get one rated for more than 4A of continuous discharge current.
Understand that your Raspberry Pi will run with your setup once you use an adequate battery, but since the input current requirements increase as the input voltage to a boost converter goes down, and any battery's terminal voltage falls as it is discharged, you will likely hit the point where the needed input current exceeds the 4A maximum of your boost converter at some point before the battery is fully discharged. If you want to use most of the capacity of LiPo cell, you will likely need a slightly beefier boost converter, but the one you have will work for now but with severely degraded run time due to much of any battery's capacity being 'inaccessible'. The exact point this will occur depends on your setup of course.
All things considered, I would like to echo the sentiment of not powering an RPI from a battery at all. The Raspberry PIs are meant to be cheap but full-featured and practical. They are not designed to be low power, and have no power management capabilities, which is a large part of why they need such a stiff power supply. It is a very poor match for any sort of battery powered application. There are dozens of similar single board computers available that do have power management (allowing them to adjust their power consumption as input voltage falls by underclocking themselves, things like that). It's beyond the scope of this question to suggest an alternative, but a quick google search for 'battery powered sbc' already returned a lot of promising results.