Altogether, there are 18 types of Guardian (not counting the 3 upgraded guardians in the DLC storyline, Another Story)
They are found throughout each map, marked with a red crossed-swords X.
Once you have defeated at least one of each type of Guardian, the achievement will unlock.
Kronos Island has four types of Guardians:
Asura (Big giant with three arms)
Ninja (Fast-striking humanoid)
Tower (Tower with spikes)
Squid (Giant squid that leaves a Light Path)
Ares Island has four types of Guardians:
Sumo (Fights in an electrical cage match)
Shark (A giant sand shark)
Strider (Like a giant radio tower, you ride grind-rings to climb it)
Tank (Red, four-legged mech that makes a whirlwind)
Chaos Island has four types of Guardians:
Fortress (Giant airship that will drop bombs then make a rail-path you have to ride to catch up)
Shinobi (Upgrade of Ninja)
Excavator (Upgrade of Tower)
Spider (Red, four-legged spider-mech that hurls Sonic sky-high)
Ouranos Island has six types of guardians:
Caterpillar (A large bug-like machine that shoots lasers)
Ghost (A Jellyfish that attaches to its statues and drains Sonic's rings; must be manually activated from its starting statue)
Kunoichi (Upgrade of Shinobi)
Master Ninja (Upgrade of Kunoichi)
Red Pillar (Upgrade of Excavator)
Silver Hammer (Upgrade of Red Pillar)
When playing the DLC story, Final Horizon, there are three further-upgraded Guardians (I don't believe these count for the achievement):
Master Ninja+
Spider+
Tank+