NOTE: To save time with this trophy, refrain from power boosting any gear until you get level 130 gear. You can boost your major artifact but only on the character you're intending to get this trophy with.
To reach Power Level 150 with a hero, you first need to get to the point where you can get level 130 gear in every slot of Epic or Legendary rarity (without power boosting), as this is the highest that will drop or be purchasable. This is a bit of a grind but you'll be a good chunk of the way there once you hit level 50 on a character. Just keep grinding, getting better and better gear. I ended up buying most of the 130 gear when it became available as I had a lot of fragments to spend. You will then have to fully power each gear item to 140. This will require a lot of resources but as long as you didn't waste too much boosting weaker gear as mentioned, you should be able to fully boost them all or get fairly close with what you have at this point. For the rare resources, you get them from the breakable crates, defeating enemies and from strongboxes. You can also buy them from vendors if needed. Upgrade modules may be more of an issue as they are rarer, you can get them from strongboxes, completing missions and defeating special marked enemies. The latter way is the best way to farm them if required. Finally, you need to max out your major artifact. This will require a lot of Polychoron which you get from completing daily assignments and villain sectors from the factions. There's a good chance you'll need more Polychoron, especially if your playtime is condensed into a few days so work on assignments as you get them while working on other trophies and you'll eventually save up enough.