[Since I received a request for an answer to this question, I'll add a second answer even though auntlori has already done the job!]
This is actually a very complex question (and a more detailed one than the eNotes format usually accommodates). What you are being asked is to infer from indirect information abstract qualities about characters who, for the most part, do not provide the knid of information sought and for whom the very present narrator (closely proximal and "intrusive"), for the most part, does not provide information relevant to these abstractions. This is "for the most part" because Austen does present at least some abstract explanation of principal characters in her novels, for example, Darcy's explanations of himself to Elizabeth (in his letter and his second proposal) and the narrator's explanations of Elizabeth as she responds to Darcy's letter (e.g., Fanny and Emma from Mansfield Park and Emma also explain themselves or are explained by the narrator).
First, how do you go about gathering information about the abstract qualities of "primary objectives in life, their philosophies, their strengths, and their weaknesses" from mostly indirect informational sources? You examine and analyze the character's behavior, remarks, and opinions and the reactions others give them. Let's apply this to a less obvious character: Lydia.
Lydia is the wayward daughter of Mr. and Mrs. Bennet. She is the youngest of the five daughters and the least seriously minded of them all. She has a charismatic and enthusiastic personality. This is apparent because she not only leads and influences her elder sister's behavior, Katie, she also attracts regimental soldiers like "flies to honey," as the saying goes. Though the youngest, it is Lydia who is allowed to go to Brighton--chaperoned by the commander's young, giddy wife--in company with the entire regiment. While there, in one of the greatest subplots of literature, Lydia throws herself on Wickham and accompany's him, against his intentions, while he once again flees from debtors.
What are Lydia's objectives in life? From her actions and remarks; from her attitudes toward matters of life (learning, flirting, productivity); from her irresponsible responses to events, we must conclude that her only objectives are to have a jolly time with as many frivolous pursuits as possible and, as a side benefit, do things before her elder sisters do them. An illustration of this sketch of her character is summed up succinctly in her remarks about the hat she buys. She has spent money foolishly on it, dislikes its detail, and declares that, once she rips it apart and re-does it, it will be pretty enough.
"I shall pull [my new hat] to pieces as soon as I get home, and see if I can make it up any better." ... And when her sisters abused it as ugly, she added, with perfect unconcern, "Oh! but there were two or three much uglier in the shop; and when I have bought some prettier-coloured satin to trim it with fresh, I think it will be very tolerable."
What is Lydia's philosophy of life? Well, no one really knows as she is not a deep thinker. She is, on the contrary, a feeler and action-taker. She responds to entertaining or amusing stimuli without thought. This trait is illustrated in the above hat incident: she was in a hat shop, wanted to respond to the stimuli of "hats," bought anything that was "hat," and will act further by recreating "hat": no thought, no logic, no consideration; simply action responding to stimuli. If this can be called philosophy, then this is her philosophy: to act. Her strengths and weaknesses are more easily seen. The former is her bright personality, the latter is her mindless headlong plunge into life. Compare her to Mrs. Bennet, using this same mode of examination and analysis, or contrast her to Jane, to round out your grasp of the objectives, philosophies, strengths and weaknesses of more than one character.
Pride and Prejudice, by Jane Austen, is about reconciling differences, among other things, and Mr. and Mrs. Bennet are different in nearly every way.
Mr. Bennet stays in his study most of the time because he is not particularly interested in the outside world and because he wants to avoid contact with most of the women in his household. He has a very dry wit and is not sparing with it; his primary targets are his wife and youngest daughters. He is not afraid to voice his opinion, but he does so in an understated way, as in the following comment to his daughter, Elizabeth:
“An unhappy alternative is before you, Elizabeth. From this day you must be a stranger to one of your parents. Your mother will never see you again if you do not marry Mr. Collins, and I will never see you again if you do.”
He is content to own what he owns and is not particularly interested in anything beyond that, either for himself or his girls; the flip side of that is that he has no ambition for himself or his family. He wants all of his girls to marry men they deserve; which is a good thing only for Elizabeth and Jane. His philosophy is to let things run as they will and make fun of the consequences.
Mrs. Bennet has enough ambition for all of them. She has one goal in life: to marry off her daughters to whatever rich men will have them. She is not particularly bright and does not seem to care that her three youngest daughters are disinterested in educating themselves.. (They, like her, are only interested in capturing rich men.) Mrs. Bennet is crude and socially gauche, but she does not seem to know or care. Unlike her husband, she is social (which is how she gets all the local gossip) and pays attention to all the details of her home which are important to her, which are not necessarily the most important things.
She wants more for her daughters, but it seems as if most of that motivation stems from her own desire for more. When she discovers that someone has rented a manor in the area, she finds out the important details and makes a plan:
"A single man of large fortune; four or five thousand a year. What a fine thing for our girls!... You must know that I am thinking of his marrying one of them.
Her philosophy is to find value in money and position, despite her own lack of them, and this works in no one's favor. Mrs. Bennet is a woman who cares about all the wrong things and had no clue that her husband constantly makes fun of her--which is probably why they have been able to stay married for more than twenty years.