This trophy requires a total of 63 skill points (21 into each branch of the skill tree), in order to get a single skill in each branch (Combat, Biotic, Tech), to Level 6. Each skill's points requirement increases exponentially based on the level.
Ex.
Level 1: 1 skill point
Level 2: 2 skill points
Level 3: 3 skill points
Level 4: 4 skill points
Level 5: 5 skill points
Level 6: 6 skill points
For a total of 21 points to max a skill out at Level 6
If you have 63 or more and just want the trophy, you can go to the Med Bay on the Tempest and re-spec your skills for 20 credits.
As soon as 3 skills are maxed out and you have saved the changes to your skill tree, the trophy will unlock.
Edit: This involves upgrading an ACTIVE skill, not a passive skill.