Here is the full list of all 21 Dogstar achievements.
Kill Otto twice in a level
Rescue 25 Comrades in a level
Destroy 3 Lifestars in a single level
Kill Otto three times in a level
Defeat the enemy homeworld of Venus
Defeat the enemy homeworld of Venus on Brutal skill level
Defeat the enemy homeworld of Venus in 2 player Co-Op mode
Get a Perfect award for kills in a single player challenging stage
Get a Perfect award for Comrades in any challenging stage
Destroy Otto using the blast from the Miner's destruction, or visa-versa.
Defeat the enemy Homeworld of Venus in the Veteran mission
Rescue 50 Comrades in a single level
Rescue 40 Comrades in a single level
Score 1 Million points
Score 2 Million points
Score 3 Million points
Defeat the enemy Homeworld of Venus at the Brutal skill level in the Veteran mission
Kill 3 standard enemies with 1 Supershot
Kill 5 standard enemies with 1 Supershot
Destroy a Lifestar with the Supershot
Get a comrade sucked into the Stargate