Does Isaiah 44:24 destroy the claims of the Trinity?

In a word, yes. Though it is hardly the only verse in the Bible to do so.

Thus says the Lord, your Redeemer,
    who formed you from the womb:
“I am the Lord, who made all things,
    who alone stretched out the heavens,
    who spread out the earth by myself, (Isaiah 44:24 NRSV)

Isaiah 44:24 is often used to question the doctrine of the Trinity because it states God “alone stretched out the heavens, who spread out the earth by myself”. However, trinitarian Christians respond to this by interpreting the verse as God speaking in a way that emphasizes His supreme power compared to the false gods of other nations, while still holding that Jesus and the Holy Spirit are also God. For comparison here is the KJV rendering which does not have the first “alone” found in the NRSV, but has the “by myself”.

²⁴ Thus saith the Lord, thy redeemer, and he that formed thee from the womb, I am the Lord that maketh all things; that stretcheth forth the heavens alone; that spreadeth abroad the earth by myself; (Isaiah 44:24 KJV)

There are of course many verses in every book of the Bible that make it clear that only God is God, and the refute the claim that the Jesus, virgin-born descendant of David and / or “holy spirit” (not a sentient being, but mainly a New Testament idiom for the figurative breath in the new life) are in any way part of God. However Isaiah 44 and 45 are particularly strong in emphasizing the absolute monotheism of Israel’s prophets, so it makes sense to point to verses like Isaiah 44:24.

It needs to be said that any argument that defends the Trinity by arguing for polytheism is a good reminder that the Trinity historically undeniable has pagan roots. This is a claim not made in an idle way but recognised by all scholars of patristics and 2nd-4th Century developments in theology. The term “pagan” would probably be replaced by “Greek philosophy”, given the unscholarly connotations of the word “pagan”, but let’s be clear that is what we are talking about: the influence of polytheistic Greek and Egyptian philosophy on Christian church understanding during the period from the ‘Apostolic Fathers’ through to Chalcedon in 381CE. Roman Catholics recognise that development, but consider it directed by the church’s divine authority. Some modern evangelicals may deny that historical reality, or more sincerely acknowledge it but then discount it saying that it does not form part of their personal belief, but the historical fact is admitted by the patristic writers themselves.

A second problem is that Isaiah clearly has a theology built on denying the existence in all forms of other elohim – there is “only One Elohim”, singular verb – the other elohim “do not exist”.

• 44:6  Thus saith the Lord the King of Israel, and his redeemer the Lord of hosts; I am the first, and I am the last; and beside me there is no God. .. 
• 44:8 Fear ye not, neither be afraid: have not I told thee from that time, and have declared it? ye are even my witnesses. Is there a God beside me? yea, there is no God; I know not any.
• 45:5 I am the LORD, and there is none else, there is no God beside me: I girded thee, though thou hast not known me:

Further Isaiah’s monotheism extends to ownership of “evil” in Isaiah 45:7 and elsewhere. (the Hebrew word “ra”, as the English word “evil”, is defined by context to mean either natural evils, or moral evils) 

• ⁷ I form the light, and create darkness: I make peace, and create evil: I the Lord do all these things. (Isaiah 45:7 KJV)

This rules out everything that stands against pure and absolute monotheism – other gods, the Trinity, fallen angels – all opposition or plurality or diversity of supernatural power.