This pesky classical copular auxiliary is still occasionally used in Modern Japanese, and as you would expect, the title really does say all. First, we will discuss the so-called タル形容動詞 that are made with it, see how the true copular role it has manages to get used, and then focus on grammar topics relevant for high level Japanese proficiency tests such as the JLPT N1.
This defunct class of adjectival verbs have the limited bases と-連用形 and the たる-連体形. However, with more antiquated grammar, you can see the other bases. So, for completeness, the full base set is given below.
Like 形容動詞, the と-連用形 is used adverbially. The exact number of タル形容動詞 still used today is uncertain, but they are in decline. Their attributive base is also typically replaced with とした. However, in more formal writing, these adjectives pop up everywhere. Depending on the adjective, they may have acquired other legitimate attributive forms. For instance, you can use 主な and 主たる (principal/main).
The main reason is this.
An absolute maniac
There isn't a special/particular difference.
A famous tourist spot
Scorn in one's presence is the extremity of insult.
6a. 最たる例 （古風)
6b. 最も顕著な例 (もっと自然）
A magnificent figure
To speak in a cool tone.
Pure and simple bank
Base Note: Though they have no modern 終止形, when the need arises, the old たり-終止形 is replaced with the たる-連体形 followed by だ, giving たるだ.
The administrative reform is merely an order, and the (system) is still as the old state.
Archaism Note: There are still instances where the auxiliary copula verb たり is still used in Modern Japanese. As it is more emphatic, it often serves a role in formal yet serious situations. One instance is 日本よ国家たれ! (Japan, be a nation!) and its derivations.
This is a usage of above that is rarely seen but is used to emphatically emphasis a topic, and it is derived from the auxiliary たる and the adverbial/bound particle や.
The technique is terrific!
This pattern follows nouns, as you would expect, to show that a certain thing is suitable in situations such as having a certain responsibility or when one is outstanding for a certain role. Remember that what follows should show what form, role, or status something should be in to be what X or what たるもの follows.
It's only natural for a person of society to maintain salutations and time.
A gentleman must be strong.
Politicians must not make gaffes.
Teachers must pay attention to their behavior.
A president must hold a sharp mind.
The conjunctive particle たりとも is equivalent to "not even" and is interchangeable with と言えども and ではあっても. It is really on the combination of the auxiliary たる + the conjunctive particle とも, which is why it's mentioned here. This pattern should follow a counter phrase that a small or indeterminate number. However, even if the number is one, if the counter phrase implies something big like a year or a ton, then this is not applicable.
I won't allow even a single letter (being wrong).
I haven't forgotten even a single day.
25. 一年たりとも X
You mustn't lose focus for even a moment.
You mustn't slack off your Japanese practice for even a day from now on!
I don't wish for even a single yen to be wasted.
Please make it toward you are not late for even one minute.
Not one at all
Reading Note: 何人 in the last expression can be read as なにびと, なんびと, or なんぴと.