Quickly moving up the list of top players in Starpires will often require taking down empires who are more powerful than you are.  Defeating a more powerful empire through brute force will simply end in disaster and requires utilizing a bit of strategy.

Know your enemy

Gathering intelligence on an opponent before attacking.  Find out if they have defense pacts with other empires, and what the makeup is of their defending forces.  Take advantage of the strengths and weakness of different military units.  For example heavy cruisers will absolutely demolish defense stations but are not very effective against either ground troops or fighters.

Hint: If you have access to it under research, a spy satellite is a useful tool in helping to spy on a larger empire.

Wear them down with Guerilla Attacks

Guerilla attacks are very useful for wearing down the military forces of a larger opponent in preparation to invade them.  You can’t capture planets through guerilla attacks, but since they occur with no warning an empire can’t call on their allies to help protect them.  Also the smaller your force is relative to your opponent the more effective each individual military unit will be.

Gas their troops

If the are reliant on a large number of troops to defend their empire, launching chemical strikes (assuming you’ve researched the technology) to kill them off is a good strategy to weaken their defenses.

Take advantage of technology

There are a number of useful technologies which you can research that can aid your attacking forces temporarily.  Jam their communications to prevent them for calling on allies to help defend against an invasion.  Set off an EMP Blast, that will disable a large percentage (~50%) of their defense stations.  Provide an Adrenaline Boost to your military units to temporarily increase their attack strength.