The strategy when using this deck is using your weaker monsters to leverage into higher-leveled monsters with effects that deal with your opponent's monsters. Since your high-leveled monsters are relatively weak compared to other monsters of the same level, Beatdown helps you attack over any monster you were not able to get rid of with effects.
Gusto Griffin is the quickest way to bring out your high-leveled monsters. When sent from hand to graveyard (even as a cost) he allows you to special summon a WIND Psychic-type monster from your deck no matter the level. Although his effect does not work alone and you need another card to combo with him by sending him to the graveyard. The upside of this is that, as a cost, he can immediately replenish himself so that you lose no card advantage.
Here are the cards you can use to discard Gusto Griffin. Tribute to the Doomed allows you to destroy 1 monster on your opponent's side of the field. You can use this to deal with one of your opponent's monster and then use the effect of the monster you special summoned with Gusto Griffin to deal with another monster your opponent controls, netting you some advantage and possibly opening for an OTK. You can special summon The Tricky for a decent beater on the field by discarding 1 hand card. With the other monster you special summon plus your attack boost from Beatdown, this could allow you to OTK.
Aside from discarding Gusto Griffin you can also Use these monsters to bring out Reeze and Space-Time Police. Unlike Gusto Griffin, Gusto Thunbolt and Serene Psychic Witch's effects activate when they are destroyed on the field. This makes them slower than Griffin but are able to activate on their own without needing another card to combo. Thunbolt special summons a WIND Psychic monster after the battle phase he is destroyed by battle and sent to the graveyard. This could also be used to combo with Reeze to take your opponent's monster and special summon a monster from your deck. Serene Psychic Witch banishes Reeze or another copy of herself from your deck which is then special summon during your next standby phase.
These are the monsters you will use for your power plays. Reeze switches control of 1 Gusto monster you control with a monster your opponent controls. Give your opponent control of Gusto Thunbolt so that you can special summon another monster from your deck when he is destroyed. Otherwise you can also give your opponent control of Reeze which would also be a good price for taking an opponent's boss monster. Space-Time Police banishes a face-up card your opponent controls when he is special summoned. This opens your opponent up to OTKs when you banish a monster, and could also be good disruption by banishing a key card. You can use this to get rid Amazoness Onslaught without triggering it's revival effect, Banish Wiz, Sage Fur Hire to get over your opponent's wall, etc. Although the card you banish will be set to your opponent's field once Space-Time Police leaves the field.