"Nepotism" means favoritism or bias. "Perfidious" means treacherous or betraying. "Solipsism" means a theory that only the self exists. "Resolute" means determined or strong-willed. "Prudence" means caution or carefullness. "Reclusive" means unsocial or isolated. "Skepticism" means  doubt or disbelief. "Ubiquitous" means ever-present or pervasive. "Parity" means equality or balance. "Scathing" means nasty or critical in remarks.

Clearly, the use of the adverb "most" indicates that the sentence pertains to a very significant type of loss. The term "loss" can mean merely something that is lost or no longer held in possession, though it could also mean, more strictly, a financial loss. Either sense works in this sentence, though the latter is perhaps more appropriate, given the talk of work and success. In any case, several answers could function as a potential answer for the first blank; however, only "devastating" has a strength that really matches the adverb "most." Something "devastating" is something causing great destruction or shock. Although the second blank could indicate that luck (or something else) is also necessary, it is best to stay with the closest meaning implied by related words in the sentence. The sentence implies that hard work will help to recover from such devastating losses. This would presumably mean that devotion or dedication would likewise help in such a process of recovery.

We know funerals are usually sad occasions, so the adjective that we pick for the first blank should mean something like "sad." Either "melancholy" (sad and pensive) or "doleful" (mournful; expressing sorrow) would be a good choice for the first blank. For the second blank, we need a noun that refers to a speech given at a funeral. While both dirges and eulogies are given in the context of funerals, dirges are songs, while eulogies are speeches or writings. Since the sentence specifies that the noun involved people speaking, "eulogy" is the better choice, and the correct answer is "melancholy . . . eulogy."

Since decades have passed when his works are rediscovered, the only answer for the second blank that makes sense is "posthumously," after his death. Acumen means sharpness and skill, and the author is now thought of as a good and sharp writer.

The first blank is "lacerations," because, of the choices, only lacerations weep on the forearm. The second blank is "credible" because the lacerations support the young man’s claim to have been beaten.

A "bombastic" dictator (that is, an arrogant dictator) is not likely to cower or be servile; neither is "tardiness" likely to whip a mob into a frenzy. A "harangue," or noisy attacking speech, is very likely to rouse a mob, but only if that mob is comprised of gullible people. Gullible people are typically not "incredulous," "skeptical," or "objective." The second blank is therefore "credulous."

An "aerie" is a nest or habitat built high above the ground. "Deleterious" means harmful, often in a subtle way. As eagles live in trees, it makes sense that logging can have a negative effect on their habitats.

To be "palatial" means to resemble a palace, often in size. The Taj Mahal only resembles a palace, and is in fact a "mausoleum," or a building that houses tombs.

The structure of the sentence indicates that the first word is a noun and the second word is an adjective that describes Napoleon’s nature. Moreover, the second word is “confirm[ing]” or supporting the first one. A "promulgation" is an announcement, and Napoleon’s claim that he will take over all of Europe would confirm his "headstrong" or stubborn and willful nature.

The phrase "formal structure" is a clue to the first word. "Pedantic" is the correct option, meaning overly concerned with formal rules and details. As the scientists benefitted from this, they performed their work well—so "alacrity," meaning liveliness or eagerness, works here.