Towards the end of the Hades level you will come to two spinning columns with all kinds of wonderful spikes protruding outward. The first spinning column is the only one you need to climb without getting hit for this trophy to pop.
The best advice I can give it to be patient and take your time. Each section spins the opposite of the previous, and staying in-between sections can be wonderful safe havens (no spikes). There are either 4 or 5 sections for each of the two columns to get through before you reach the top.
If you do take damage, the game autosaves at the bottom, so you can press start and select the "Restart at Last Checkpoint" option, and try again.PLEASE NOTE:
There are claims that this trophy may simply require you reach the top. If you get hit by the spikes then you just fall to the bottom and have to climb it again. The trophy MAY just require you get to the top, which requires not getting hit anyway, so you may fall to the bottom a few times, make it to the top and still get the trophy (I am not sure since I did the checkpoint thing a couple of times
). If anyone can confirm this please write it in the comments below.UPDATE:
It has been confirmed by munchmagic1986 that all one needs to do is reach the top of the first column, essentially making this a story related, and unmissable, trophy. If you fall there is no need to restart at the checkpoint.