Ok, let's brush off all the dust and spittle and try again ...
If TofE purports that organisms evolved from simpler to more complex forms, how is it possible that these mechanisms could have seemingly completely bypassed the 2nd law of thermodynamics?
Ok, we're going to have to elaborate "TofE purports that organisms evolved from simpler to more complex forms." What TofE actually purports is:
1. Individuals are not reproduced as exact replicas, but with genetic differences.
2. The environment selects for some of these differences and selects against others, causing the population's genetic makeup to change.
3. Accumulation of change over time causes gross structural changes so that in time a daughter population emerges which is different enough so that it can no longer undergo genetic intermixing with the parent generation.
4. Typically, the daughter population is also able to expand into a new niche because of these changes. [You could say that it is "more advanced", but that depends on how you measure advancement.] But whether or not this happens,
5. Change continues to occur within the daughter generation as in step 1.
etc. etc.
Now, there might be any amount of reasons for this cycle of processes to be impossible, but the 2nd Law of Thermodynamics isn't one of them. None of these processes individually violate it, so how can the overall process violate it?
1. Reproduction doesn't violate the 2nd Law of Thermodynamics. Of course, I haven't personally verified this, but I have it on expert testimony (not least of which is the fact that I exist).

Neither does mutation and the carrying of errors by young.
2. Environmental selection for a given trait doesn't violate the 2nd Law of Thermodynamics. It's just a matter of some animals being able to reproduce more, and some less. No perpetual machine nonsense happening here.
3. Accumulation of change is nothing more than step 1, repeat a few thousand times. Let's say I have change A in me. My son inherits change A, and in turn has his own change B as well. His son, my grandson, might have three changes. And so on. Well, there might be any number of reasons this might not work, but physically speaking the 2LoT doesn't prevent me from giving birth to something different from me, or prevent my distant descendant from giving birth to something a whole lot different from me.
4. Again, no physical law prevents birds from taking over the sky or land plants from taking over the sea once they have evolved.
And there you go. Evolution, whatever else it can't handle, doesn't have a problem with the 2nd Law of Thermodynamics. Why should it?