Hi. I have made a video guide for this. Please note that the scenarios the game randomly gives you after every 5 barrels are random most of the time, and the video is about giving you tips on how to clear some of these sections.
My suggested strategy for this:
Select Shield and Deathless from the selection at the beginning. The rest don't matter.
Now, your aim is to last until 125 barrels with the shield intact.
When you reach 125 barrels, get hit and lose your shield on purpose. Now, you need to stay alive with 1 hit point until 140 barrels, then you should be able to pick up the Deathless power-up and finish the last 10 barrels easily. The next power-up always spawns after breaking 15 barrels and you need to lose the shield to get the progress done towards the next power-up. That is why you need to lose the shield at 125 barrels.
Why would you do this? Because the last 10 barrels from 140 to 150 are often insanely painful and annoying and people have commented that this is the part when they usually fail the run. Why collect 140 barrels just to die at the end?
My goal in this video was to last until 125 barrels with the shield intact but I messed it up. But you should try to last until then. I was getting moderately skilled at this game when I recorded this video, so you will have to do some practise runs either way to get this done.
I have a decent amount of tips in the video, I suggest you read all of them instead of ignoring them.