Me alegra haber tachado ya todo lo necesario de la lista de la compra.

Me alegra means it makes me happy / I’m glad and is a very common way to react to an action or situation.

Here, the thing causing the feeling is haber tachado ya todo lo necesario...
So the structure is:

• Me alegra + infinitive / clause
• literally: It pleases me / It makes me happy to...

By contrast:

• Estoy alegre = I am cheerful
• Estoy contento/a = I am happy / pleased

Those are possible in other contexts, but me alegra is especially natural when you want to say that a specific fact or completed action makes you happy.

For example:

• Me alegra verte. = I’m happy to see you.
• Me alegra haber terminado. = I’m glad to have finished.

Haber tachado is the perfect infinitive. It refers to an action that happened before the feeling in me alegra.

So:

• Me alegra tachar... would suggest being happy about the act of crossing things off in general or as it happens.
• Me alegra haber tachado... means I’m glad to have crossed off everything already — the action is completed.

This is very similar to English:

• I’m glad to cross things off → more general / less natural here
• I’m glad to have crossed everything off → completed action, which matches the Spanish sentence

Tachar usually means to cross out or to strike through something written on paper.

In a shopping-list context, tachar algo de la lista means:

• to cross an item off the list
• to mark it as done / bought

So haber tachado ya todo lo necesario means the speaker has already crossed off all the necessary items.

Ya means already here.

It appears between tachado and todo lo necesario:

• haber tachado ya todo lo necesario

That placement is very natural in Spanish. It modifies the completed action: the speaker has already crossed everything off.

Other positions are sometimes possible, but this one is the most straightforward and idiomatic here.

Compare:

• Me alegra haber tachado ya todo lo necesario. = natural
• Me alegra ya haber tachado... = possible in some contexts, but less neutral here
• Me alegra haber ya tachado... = generally less natural

Lo is doing an important job here.
Lo necesario means what is necessary or the necessary things.

So:

• todo lo necesario = everything necessary / all that is necessary

You often see this pattern:

• lo importante = what is important
• lo bueno = the good thing / what is good
• lo necesario = what is necessary

Without lo, todo necesario does not work naturally in standard Spanish.

Spanish often prefers a more compact structure.

• todo lo necesario = everything necessary
• todas las cosas necesarias = all the necessary things

Both can make sense, but todo lo necesario is much more natural and idiomatic. It sounds less heavy and more elegant.

It is a very common Spanish way of expressing an abstract set of things defined by an adjective.

With tachar, Spanish commonly uses tachar algo de una lista:

• tachar algo de la lista = to cross something off the list

The idea is that the items are removed from the active list by crossing them out.

So:

• taché el pan de la lista = I crossed bread off the list

Using de is the normal preposition with this meaning.

Yes, la lista de la compra is very common in Spain.

It means:

• shopping list
• literally: the list for the shopping

In other varieties of Spanish, especially in Latin America, you may often hear:

• la lista del supermercado
• la lista de compras
• la lista para comprar

But in Spain, la lista de la compra is very standard and natural.

In Spain, la compra often means the shopping / the groceries as a general activity or errand.

So:

• hacer la compra = to do the shopping / grocery shopping
• la lista de la compra = shopping list

English speakers sometimes expect a plural idea like shopping(s) or purchases, but Spanish uses the singular noun la compra in this common expression.

Not in this exact structure.

After me alegra, if you want to refer to your own completed action in this way, the normal form is the infinitive construction:

• Me alegra haber tachado... = I’m glad to have crossed off...

If you use he tachado, you would need a different sentence structure, for example:

• Me alegra que haya tachado todo lo necesario. = I’m glad that I have crossed off everything necessary.

But that sounds less direct and less common when talking about your own action.
So in this sentence, haber tachado is the most natural choice.

Spanish often leaves out subject pronouns when they are understood from the verb or the context.

Here, yo is not needed because the sentence already makes sense without it:

• Me alegra haber tachado ya todo lo necesario...

The person doing haber tachado is understood to be the same speaker who says me alegra.

Spanish avoids pronouns more often than English does, especially when there is no need for emphasis or contrast.

Exactly.

The thing that makes me happy is the whole infinitive phrase:

• haber tachado ya todo lo necesario de la lista de la compra

An infinitive phrase acts like a singular idea, so the verb is singular:

• Me alegra... not Me alegran...

Compare:

• Me alegra terminar pronto. = Finishing early makes me happy.
• Me alegran las buenas noticias. = Good news makes me happy.

In your sentence, the subject is not plural items; it is the single idea of having crossed everything off.

Yes, depending on the nuance.

Some possible alternatives are:

• marcar = to mark
• quitar = to remove
• anotar = to write down, not the same meaning
• borrar = to erase, usually not the same as crossing off

But for a list, tachar is especially precise because it specifically suggests putting a line through the items once they are done or bought.

So tachar de la lista is one of the best verbs here.