The trick behind completing the game without deaths is to rely on getting fuel drops for the helicopters in area 3 and 4. There is a good deal of RNG to get this to work, but the game mechanics governing the drops are well understood, which has allowed manipulation at least to some extent of the fuel drops. See fuel drop manipulation for more information. It's possible, at least in theory, to beat the game without deaths even without relying on the fuel drops, but it would be much, much slower and will not be described here.

Below are shown the parts that will be different from the death abuse route and some more conservative and safer strats. The latter can be justified by the fact that this category is significantly more RNG-dependent to complete than a death-abuse run.

Area by area description

Area 3

Tank - https://www.youtube.com/watch?v=vjMInsi2xP8
Easy and much safer than passing this section on foot. It's ~4.5 secs slower in the tank though.
If you get soldiers on foot behind your tank, it's quite likely that they will shoot you in the back once you have left the tank. If that happens, you will more or less be required to stop and get them in front of you or reverse to take them out.

Foot2 - https://www.youtube.com/watch?v=wEwo34_OEcM
The end of the water section is quite often plagued by random bullet-shooting soldiers, but it's overall not too bad. It's worth pointing out that by walking over the corners in the water section, you save a little time compared to walking around them.

Foot3 - https://www.youtube.com/watch?v=ko3R4ayFAB8
Mostly predictable, but still quite long and some sections are quite risky because of random shooting soldiers that can appear. The final section before the helicopter is constructed to help getting the fuel drop later on while in the helicopter. A more thorough description of how this works is found in fuel drop manipulation.
Using the tank is of course a bit safer than continuing on foot (but actually also adds a few risks). For illustration, the tank route is shown here: https://www.youtube.com/watch?v=-iI2cIpM6yc. It's slower by over 15 seconds.

Helicopter - https://www.youtube.com/watch?v=9WtWQ96FpVM
- The fuel drop from the first tank can be manipulated. A more thorough description of how this works is found in fuel drop manipulation.
- When exiting the helicopter, you'll be facing the direction you were last flying in. By reversing just before leaving the helicopter, you can immediately start walking down instead of having to do the half-circle turn if you had been facing up.
- The boss takes 5 hits (the hitbox is huge) and then you need to toss a grenade at the floor below the desk to reveal the exit. The staircase takes up two blocks and can be in one of several locations below the desk. The location is random and depends on the timer and player input leading up to that point. It doesn't appear to possible to manipulate the location, but the underlying mechanism is not known. With the current knowledge, the best you can do is to throw one grenades from the left side to cover the possibility of the stairs being on the right side. If that doesn't work, turn around and toss a grenade to the left from the opposite side of the desk to cover the remaining possibilities. You should never need more than 2 grenades to cover all possibilities.

Area 4

Tank - https://www.youtube.com/watch?v=WK2zVINfCjs
If you carefully follow the path shown here, there should be no problems and it's much, much safer than passing it on foot. The time difference is around 8 seconds though.

Foot2 - https://www.youtube.com/watch?v=l0x5SG6gdOM
Random enemies can appear on the left side of the water section, but are usually quite easily dealt with when it's the case. The rest is not random and quite easy to execute. The route through the barrel area until the helicopter is constructed to maximize the odds of getting a fuel drop for the helicopter. A more thorough description of how this works is found in fuel drop manipulation.

Helicopter - https://www.youtube.com/watch?v=ixzhtN51Zs4
The last "missile turret" is very random and somewhat "intelligent" (moves in ways to avoid your shots), so care has to be taken here. The rest is fairly easy to execute. However, there is a small chance that weird things happen along the way. It can be enemies that spawn in slightly different locations and therefore being out of reach or a grenade that is tossed from one of the walls that can hit. This is rare though. The route shown here is made to be as safe as possible (it's possible to take a straighter route at the cost of some risk in some places).
The last boss takes 10 hits. Occasionally, the boss takes more grenades to destroy. Some observations of this behavior is described in the death abuse route.