To avoid this issue again you have to make sure that the amount of money withheld from your paychecks, and the 25% withheld by the company for the RSUs hit the 110% safe harbor. When you pay your taxes in April, take note of the total amount of taxes you were responsible for. Then make sure that 110% is withheld.
You need to look at IRS Pub 505 for 2019:
In most cases, you must pay estimated tax for 2019 if both of the
You expect to owe at least $1,000 in tax for 2019, after subtracting your withholding and refundable credits.
You expect your withholding and refundable credits to be less than the smaller of:
a. 90% of the tax to be shown on your 2019 tax return, or
b. 100% of the tax shown on your 2018 tax return. Your 2018 tax
return must cover all 12 months.
Note. The percentages in (2a) or (2b) just listed may be different if
you are a farmer, fisherman, or higher income taxpayer.
Higher Income Taxpayers
If your AGI for 2018 was more than $150,000 ($75,000 if your filing
status for 2019 is married filing a separate return), substitute
110% for 100% in (2b) under General Rule
This doesn't mean that you won't have to make a big payment it just means that you will avoid the penalty.
If in 2019 the RSUs aren't a significant portion of your pay, then it might be hard to reach the 110% threshold. In that case you will have to make sure reach one of the other safe harbor values. But this could mean that you will have to file and pay estimated taxes 4 times a year to make sure you meet the 90% of tax to be shown on your tax return.
You could also ask your company to withhold at a higher rate, but they might not do that. I know a company that i used to work for would asks employees who are cashing in many weeks of vacation when they leave the company if they want it treated at a bonus and withheld at 22% or do they want it added to their last paycheck, and thus have it withheld at a higher rate.
For the taxes that are due in April 2019, you need to make sure that you are taking every item you can. make sure you claim all your contributions to charity, and go through the list of other allowable deductions to make sure you havn't missed anything.
Because it already February most options are now closed. If you can contribute to a deductible IRA for 2018, then do so. But if it is not a deductible IRA it won't help you to avoid or lessen the penalty. Another option is if you had a HSA in 2018, and you didn't maximize your contribution, then do so before the tax deadline.