Learn Spanish (Latin America): Él ni siquiera pudo alcanzar el trapecio.

In Spanish, when a negative phrase like ni siquiera (not even) comes before the verb (pudo), you do not need to add no. If you wanted to put ni siquiera after the verb, you would need to create a double negative: Él no pudo alcanzar el trapecio ni siquiera.

What does siquiera mean on its own? Could I leave out the ni?

To say "not even," you must use the full phrase ni siquiera. On its own, siquiera usually means "at least" in an affirmative context, or it relies on another negative word appearing earlier in the sentence to complete the meaning.

Why use the preterite pudo here instead of the imperfect podía?

We use the preterite pudo because this describes a specific, completed attempt in the past where he tried and failed to reach the trapeze. If we used the imperfect podía, it would sound like a general, ongoing inability over a period of time, rather than a single event.

Can alcanzar be used for reaching abstract things, or just physical objects like a trapeze?

Alcanzar is very versatile. You can use it for physically reaching or catching something, but it is also the standard verb for reaching abstract goals, such as achieving a dream (alcanzar un sueño) or reaching a certain level or status.