Prove that things are different from when you set up your irrevocable trust to receive the proceeds of your life insurance, so that changes in it are justified. For example, at the time your set it up, you were happily married. Today, after a messy divorce, you are happily remarried with more children, and you want to take care of your new family. Besides, the one child of your first marriage is wealthy and doesn't need your inheritance. Or, you are still happily married but your irrevocable trust names your child, now in his 20's, as its beneficiary if your spouse is no longer alive, and that the child should receive the proceeds in one lump sum. You'd like to change your trust to pay staggered amounts instead, since you think he is likely to spend it quickly, otherwise.
Show that the lawyer who drafted your irrevocable trust did not include what you wanted in it. A claim that such errors in drafting occurred is grounds for making changes.
Consider setting up a new irrevocable trust, and have the trustee transfer the principal of the old trust to the new one. This method can be used only in a few states. This is a good strategy so long as the new trust provides relatively the same rights to the beneficiaries that the old one does. For example, this is a good way for surviving beneficiaries, like children, to be limited in what they receive because the trustee is empowered to dole out the proceeds to them instead of paying them all at once.
Change the contents of your irrevocable trust by getting the approval of all the trust's beneficiaries and the trustee. This is allowed by most states, but it must be approved by the court in your area, as well. If any of the beneficiaries are minors, their interests must be protected by a guardian who is approved by the court. To get the court's approval to make changes, you need to prove that those changes are in their best interest.