Skill Prisoner is excellent to protect Leo from many Toolbox monsters (Generic Xyz / Tenki + Bear) for 2 turns. Set the trap after using Leo's effect the 1st time, activate it next turn to protect Leo; Use Leo's effect again and activate the trap from your grave during what could be your opponent's last turn, gaining the final counter next turn.
Remember that this card specifies Spell & Trap Card Zone. As such, you may have a Field Spell while using this card's effect.
It is very hard to make a deck that can both easily summon and continuously protect this card. Try one with few level 8s and uses spells that change monster levels like "Galaxy Queen's Light". Most of the other monsters should have effects that stop attacks and effects that remove this card from the field like the ones mentioned in tips above. "Stardust Dragon" is excellent for this monster because he's a valid Xyz Material as well as a safeguard against destruction effects.
"Prime Material Dragon" is an ideal card to protect you from opponent card effects without using spells/traps. Save drawn spells and traps in the hand as ammunition for Prime Material Dragon's effect to ensure a counter.
If "Number 88: Gimmick Puppet of Leo" is deprived of Xyz Material, "Overlay Regen" and "Spirit Converter" can be used to keep an auto-win viable.
One possible deck option that could work well with this card, is to add this card to an old "Beast Machine King Barbaros Ür" deck heavy on "Beast King Barbaros." This would allow for several easy plays to get 3 level 8 monsters on the field. Usually two "Beast King Barbaros" (one revived from the graveyard and one summoned at 1900 attack) and one "Beast Machine King Barbaros Ür". These monsters effects, if used properly could also be used to protect this card.
Defenses against this card
You can use "Counter Cleaner" to remove any Destiny Counters this card may have accumulated, leaving your opponent unable to muster enough replacements to win the duel by this card's effect without first replenishing its Overlay Units.
Likewise, you can go after the Overlay Units directly with cards like "Overlay Eater" or "Rank-Up-Magic Barian's Force", preventing this monster from having enough of them to gain the Destiny Counters it needs in the first place.
Use a card that bounces ("Compulsory Evacuation Device") or flips this card face-down ("Book of Moon") to get rid of its threatening Counters.
You can actually use your opponent's "Destiny Leo" against him by taking control of it with cards like "Creature Swap", "Enemy Controller" and "Mind Control". Whoever controls this card when the third Counter is placed wins the duel.