Star Trek Online

New Romulus is an open world area you will unlock during the New Romulus story arc. You can start earning this achievement as soon as you beam down to the planet. The accolades require are all exploration based so there is no combat involved, though enemies might attack you while you are looking for the objective. Here is a LINK to the STO wiki that explains what is required for each of the accolades.

The achievement is for earning the accolade Colonizing New Romulus which is found under Exploration Accolades once you have earned one of the required accolades. After you have found all 10 of the exploration spots you will earn Colonizing New Romulus and the achievement will pop.

The link that I have provided leads to a very good description of what is required and a map of the area. I highly recomend using it. For completion's sake I will post all the descriptions below from the link and add in anything that helped me to earn them.
 

• Colonizing New Romulus
  • Building the Gates: Approach the doors of the embassy.
  • Staging Area Quartermaster: Climb the building that the Romulan Historian (The one for the History of New Romulus achievement) is standing in front of. Use the rocks behind the building.
  • To Bodly Jump: Head south from the Staging Area, jump off the broken bridge into the Atlai river.
  • Why Are You Climbing a Rock Formation?: Climb the rock formation west of the Isha Forest. There is a gently sloping rock at the start of the formation that you can use to get up the rest of it.
  • New Romulan Historian: South of the Transporter Pad in the Hwael Ruins, there is a one story structure. As you are running south you will see rocks to the right of it. There is a sloped rocked you can run up to get above the structure and jump on it.
  • A Hwael of a Good Time: This is the toughest one because of how bad the jumping physics are. Go up the huge tree fallen tree in the south of Hwael Ruins and climb up to the highest point of the rock to the right. You can not just walk up the rock from the tree. Instead of you have to do a kind of running jump on to the sloped side of the rock. If you can jump far enough onto the slope your character will stick and you can walk up the rest. If you do not jump far enough your character will just slide off. This will take multiple attempts to get the right angle.
  • Bridge Troll: There is a large bridge south of Vasham Peaks. Run across the bridge so you are facing north. Go down the left side of the bridge to the arch underneath it. Climb on the arch until you get to the stone pillar. You can skirt around the leftside edge of the stone piller if you are careful. Once you get to the arch on the other side of the stone pillar the accolade will pop.
  • Brave New Waterfalls: Go back to where you started for Bridge Troll on the south of the giant bridge. This time go down the rocks on the right side of bridge. There is a path you can follow around the cliff. Jump into the waterfall.
  • The Easy Hard Way: Near the river mouth by the GIANT WHATEVER THAT IS, climb the rocky path up to Vastam Peaks.
  • Master of Vastam: Northern part of Vastam Peaks, near the transporter camp.